Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Jian Xu The short pulse equation is an important integrable equation, which can be solved by the so-called inverse scattering method with the help of a Wadati–Konno–Ichikawa type Lax pair, in nonlinear optical field. In a recent paper Xu (2018), we obtain the leading order long-time asymptotics of the initial value problem for the short pulse equation under the assumption that the scattering data a(k) has no zero on the above half-plane for the complex variable k. In this paper, we show two different results for the zeros of the scattering data a(k) with the finite compact support initial value. Firstly, in the linear initial value case, a(k) has no zeros. Secondly, in the even box-type linear initial value, a(k) has infinite simple zeros with the same image part on the upper-half plane.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Hai-qiong Zhao The modified Volterra lattice equation with nonholonomic constrain has been considered in this paper. The integrability of the deformed model has been demonstrated by providing a Lax pair. Applying the gauge transformation to the Lax pair, we establish Darboux transformation theorem for the nonholonomic deformation equation. Some analytic solutions of the system are obtained via the one-fold and two-fold Darboux transformations. The deformation on explicit solutions exhibits different curvy profiles and propagation trajectories that were not found in modified Volterra lattice equation.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Chein-Shan Liu, Chih-Wen Chang The inverse conductivity problem of a nonlinear elliptic equation is solved by using two sets of single-parameter homogenization functions as the bases for solution and conductivity function. When the solution is obtained by solving a linear system to satisfy the over-specified Neumann boundary condition on a partial boundary, the unknown conductivity function can be recovered by solving another linear system generated from the governing equation by collocation technique. The maximum absolute error of the recovered conductivity is smaller than the noise being imposed on the Neumann data. The superposition of homogenization functions method (SHFM) is quite accurate to find the whole solution and the conductivity function, and the required extra data are parsimonious.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Dianli Zhao, Haidong Liu This paper formulates a new switched two species chemostat model and discusses the coexistence behavior in the chemostat. A complete classification on the single-species chemostat is carried out firstly, where the stationary distribution with ergodicity is derived to exist and be unique. Then, based on the obtained stationary distribution and the comparison theorem, we put forward some sufficient conditions for the coexistence of microorganisms in the two species chemostat with Markov switchings. Moreover, when the species coexist in the deterministic chemostat for each state and have the same break-even concentrations for all states, they are proved to coexist still in the switched chemostat, which randomized the results of the classical deterministic chemostat. Results in this paper show that Markov switchings can contribute to coexistence of the two species.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Jianguo Huang, Lili Ju, Bo Wu In this paper we propose a fast compact exponential time differencing method for solving a class of semilinear parabolic equations with Neumann boundary conditions. The model equation is first discretized in space by a fourth-order compact finite difference scheme with an appropriate treatment of the boundary condition, the resulting semi-discretized system is then diagonalized with fast Fourier transforms, and further expressed in a temporal integral formulation by the use of exponential integrators according to the Duhamel principle. The fully discrete scheme is finally obtained by using multistep interpolations for the nonlinear terms and exact evaluations of the underlying integrals. Some numerical experiments are performed to demonstrate the accuracy and efficiency of the proposed method.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yan Tian, Shuhuang Xiang Prolate spheroidal wave functions of order zero (PSWFs) are widely used in scientific computation. There are few results about the error bounds of the prolate interpolation and differentiation. In this paper, based on the Cauchy’s residue theorem and asymptotics of PSWFs, the convergence rates are derived. To get stable approximation, the first barycentric formula is applied. These theoretical results and high accuracy are illustrated by numerical examples.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Ruihong Ji, Hongxia Lin, Jiahong Wu, Li Yan This paper examines the stability problem on perturbations near a physically important steady state solution of the 2D magnetohydrodynamic (MHD) system with only partial dissipation. We obtain two main results. The first assesses the asymptotic linear stability with explicit decay rates while the second affirms the global stability in the Sobolev space H1 setting.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Chao Li, Qilong Guo, Meimei Zhao In this paper, the (2+1)-dimensional time-fractional Schrödinger equation is studied within the Jumarie’s modified Riemann–Liouville derivative framework. By introducing the fractional complex transform, the (G′G)-expansion method is used to find the explicit analytical solutions of this equation. Abundant new exact solutions including the hyperbolic functions, the trigonometric functions and the rational functions are derived. These solutions are new and significant to reveal the pertinent features of the physical phenomenon.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yanfeng Guo, Donglong Li, Junxia Wang In this paper, traveling waves with different frequencies and velocities can be constructed by three wave method. Some new exact solitary and periodic solitary solutions are obtained for the Fifth-Order Sawada–Kotera equation using three wave type method via Hiröta bilinear form. The solutions investigated by three wave method are more than solutions by others method such as homoclinic test method.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yuezheng Gong, Jia Zhao In this letter, we present a novel class of arbitrarily high-order and unconditionally energy-stable algorithms for gradient flow models by combining the energy quadratization (EQ) technique and a specific class of Runge–Kutta (RK) methods, which is named the EQRK schemes. First of all, we introduce auxiliary variables to transform the original model into an equivalent system, with the transformed free energy a quadratic functional with respect to the new variables and the modified energy dissipative law is conserved. Then a special class of RK methods is employed for the reformulated system to arrive at structure-preserving time-discrete schemes. Along with rigorous proofs, numerical experiments are presented to demonstrate the accuracy and unconditionally energy-stability of the EQRK schemes.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Mengchao Wang, Qi Zhang This paper is devoted to the existence of solutions for a singular critical semilinear elliptic equation. Some existence and multiplicity results are obtained by using mountain pass arguments and analysis techniques. The results of Ding and Tang (2007) and Kang (2007) and related are improved.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Ai-Li Yang Recently, by applying the minimum residual technique to the Hermitian and skew-Hermitian splitting (HSS) iteration scheme, a minimum residual HSS (MRHSS) iteration method was proposed for solving non-Hermitian positive definite linear systems. Although the MRHSS iteration method is very efficient, it is conditionally convergent. In this work, we further study the convergence of the MRHSS iteration method, and show that it can unconditionally convergent if its parameters are determined by minimizing a new norm of the residual. Numerical results verify that the MRHSS method discussed in this work is also very efficient.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yong Zhou The purpose of this paper is to prove the existence theorems of the nonoscillatory solution for higher order neutral dynamic equations on time scales. Our results improve and generalize the recent known results by removing some restrictive conditions.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Meiqiang Feng Applying a new fixed point theorem due to Radu Precup, this paper investigates the existence and multiplicity of nontrivial radial solutions of coupled system of k-Hessian equations.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yanling Zhu, Kai Wang, Yong Ren, Yingdong Zhuang In this paper, we investigate the global existence of almost surely positive solution to a stochastic Nicholson’s blowflies delay differential equation with regime switching, and give the estimation of the path. The results presented in this paper extend some corresponding results in Wang et al. Stochastic Nicholson’s blowflies delayed differential equations, Appl. Math. Lett. 87 (2019) 20–26 .

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Jishan Fan, Liangwei Wang, Yong Zhou This paper proves a regularity criterion for a new density-dependent incompressible Hall-MHD system with positive density.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yibin Ding, Xiang Xu In this paper, a strategy to design a functional for inverse problems of hyperbolic equations is proposed. For an inverse source problem, it is shown that the designed functional is globally strictly convex. For an inverse coefficient problem, we can only prove that it is strictly convex near true solution. This strategy can be generalized to other inverse problems, as long as Lipschitz stability is given.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Jiguang Rao, Jingsong He, Dumitru Mihalache, Yi Cheng In this letter, we investigate the dynamics and various interaction scenarios of localized wave structures in the Kadomtsev–Petviashvili (KP)-based system. By using a combination of the Hirota’s bilinear method and the KP hierarchy reduction method, new families of determinant semi-rational solutions of the KP-based system are derived, including lump solitons and rogue-wave solitons. The generic interaction scenarios between distinct types of localized wave solutions are investigated. Our detailed study reveals different types of interaction phenomena: fusion of lumps and line solitons into line solitons, fission of line solitons into lumps and line solitons, a mixture of fission and fusion processes of lumps and line solitons, and the inelastic collision of line rogue waves and line solitons.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yu Tian, Min Zhang The aim of this paper is to study the existence of solutions for second-order differential equations with instantaneous and non-instantaneous impulses. Applying variational method, the existence result is obtained.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Shujun You, Boling Guo We consider the initial–boundary value problem for the KdV–Burgers equation posed on a bounded interval [a,b]. This problem features non-homogeneous boundary conditions applied at x=a and x=b and is known to have unique global smooth solution.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Jiu Liu, Tao, Liu, Hong-Ying Li With the help of the Nehari manifold, a Kirchhoff type equation involving two potentials was considered. Under new assumptions, a ground state solution was obtained.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Ying Kong, Le Xin, Qirong Qiu, Lijia Han In this paper, exact solutions for the modified Zakharov equations with a quantum correction are studied. We construct the periodic wave solutions for the quantum Zakharov equations by applying the dynamical systems method and F-expansion method. Moreover, when the modulus h of the Jacobian elliptic functions converges to 1, the periodic solutions will converge to the corresponding solitary wave solutions.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yuguo Lin, Yanan Zhao In this paper, we consider a regime-switching SIS epidemic model with jumps. By verifying a Foster–Lyapunov condition, a sufficient condition for the exponential ergodicity is presented. As a by-product, we determine the threshold for the disease to occur or not.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Zhongzhou Lan Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude η→0.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Hantaek Bae, Kyungkeun Kang In this paper, we provide a new regularity criterion of smooth solutions via the one component of the velocity field in various scaling invariant spaces with a natural growth condition of the L∞ norm near a possible blow-up time.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Xiangpeng Xin, Linlin Zhang, Yarong Xia, Hanze Liu In this paper, using the standard truncated Painlevé analysis, the Schwartzian equation of (2+1)-dimensional generalized variable coefficient shallow water wave (SWW) equation is obtained. With the help of Lax pairs, nonlocal symmetries of the SWW equation are constructed which be localized by a complicated calculation process. Furthermore, using the Lie point symmetries of the closed system and Schwartzian equation, some exact interaction solutions are obtained, such as soliton–cnoidal wave solutions. Corresponding 2D and 3D figures are placed to illustrate dynamic behavior of the generalized variable coefficient SWW equation.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Zhuo-Jia Fu, Sergiy Reutskiy, Hong-Guang Sun, Ji Ma, Mushtaq Ahmad Khan This study presents a robust kernel-based collocation method (KBCM) for solving multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method, Radial basis functions (RBFs) and Muntz polynomials basis (MPB) are implemented to discretize the spatial and temporal derivative terms in the VOTFPDEs, respectively. Due to the properties of the RBFs, the spatial discretization in the proposed method is mathematically simple and truly meshless, which avoids troublesome mesh generation for high-dimensional problems involving irregular geometries. Due to the properties of the MPB, only few temporal discretization is required to achieve the satisfactory accuracy. Numerical efficiency of the proposed method is investigated under several typical examples.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Bin He, Wei Yang, Fuhao Liu In this paper, we first design a coordinate transformation and derive the anisotropic material parameters of the quadrilateral thermal cloak according to the transformation thermodynamics principle. Then, since the derived parameters are inherently anisotropic, we eliminate its anisotropy by considering the effective medium theory and use a layered structure of metamaterials composed of only two isotropic materials to design the cloak device. Finally, we simulate the performance of a perfect and layered thermal cloak by the finite element method. To the best of our knowledge, this is the first work to design and simulate the performance of this quadrilateral thermal cloak by the finite element method(FEM).

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Lin Luo In this letter, we discuss a variable-coefficient Boiti–Leon–Manna–Pempinelli equation. We present its soliton solution and derive its new bilinear Bäcklund transformation through Bell polynomial technique and bilinear method. Finally, we show the variable-coefficient Boiti–Leon–Manna–Pempinelli equation is completely integrable.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Keying Song, Tonghua Zhang, Wanbiao Ma In this paper, a stochastic non-autonomous model with biodegradation of microcystins is considered. Firstly, the threshold of the model that determines whether the microcystin-degrading bacteria extinct is obtained. Then, we investigate the persistence of species: it shows that there exists a unique nontrivial positive periodic solution. Finally, we conclude our study by a short discussion.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Jamie J.R. Bennett, Jonathan A. Sherratt When one considers the spatial aspects of a cyclic predator–prey interaction, ecological events such as invasions can generate periodic travelling waves (PTWs)—sometimes known as wavetrains. In certain instances PTWs may destabilise into spatio-temporal irregularity due to convective type instabilities, which permit a fixed width band of PTWs to develop behind the propagating invasion front. In this paper, we detail how one can locate this transition when one has unequal predator and prey dispersal rates. We do this by using absolute stability theory combined with a recent derivation of the amplitude of PTWs behind invasion. This work is applicable to a wide range of reaction–diffusion type predator–prey models, but in this paper we apply it to a specific set of equations (the Leslie–May model). We show that the width of PTW band increases/decreases when the ratio of prey and predator dispersal rates is large/small.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Francesc Aràndiga, Dionisio F. Yáñez Monotonicity-preserving interpolants are used in several applications as engineering or computer aided design. In last years some new techniques have been developed. In particular, in Aràndiga (2013) some new methods to design monotone cubic Hermite interpolants for uniform and non-uniform grids are presented and analyzed. They consist on calculating the derivative values introducing the weighted harmonic mean and a non-linear variation. With these changes, the methods obtained are third-order accurate, except in extreme situations. In this paper, a new general mean is used and a third-order interpolant for all cases is gained. We perform several experiments comparing the known techniques as the method proposed by Fritsch and Butland using the Brodlie’s function, PCHIP program of Matlab (Moler, 2004; Wolberg and Alfy, 2002) with the new algorithm.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Meng Liu, Meiling Deng A tumor growth model perturbed by both white noise and Markov switching is formulated and explored. The threshold between permanence and extinction is obtained. Some effects of environmental stochasticity on permanence and extinction of the model are revealed.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Yanli Xu This article mainly explores a class of non-autonomous delayed Nicholson’s blowflies model with a nonlinear density-dependent mortality term. By combining Lyapunov function method with differential inequality approach, some novel assertions are gained to guarantee the existence and exponential stability of positive periodic solutions for the addressed model, which generalize and refine the corresponding results in some recent published literature.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Josef Diblík, Mária Kúdelčíková, Miroslava Růžičková A new criterion for the existence of positive solutions of the second-order delayed differential equation ÿ(t)=f(t,yt,ẏt), t∈[t0,∞) is given with applications to linear equations. Open problems for future research are formulated.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Xia Wang, Libin Rong HIV infection persists despite long-term administration of antiretroviral therapy. The mechanisms underlying HIV persistence are not fully understood. Direct viral transmission from infected to uninfected cells (cell-to-cell transmission) may be one of them. During cell-to-cell transmission, multiple virions are delivered to an uninfected cell, making it possible that at least one virion can escape HIV drugs and establish infection. In this paper, we develop a mathematical model that includes cell-to-cell viral transmission to study HIV persistence. During cell-to-cell transmission, it is assumed that various number of virus particles are transmitted with different probabilities and antiretroviral therapy has different effectiveness in blocking their infection. We analyze the model by deriving the basic reproduction number and investigating the stability of equilibria. Sensitivity analysis and numerical simulation show that the viral load is still sensitive to the change of the treatment effectiveness in blocking cell-free virus infection. To reduce this sensitivity, we modify the model by including density-dependent infected cell death or HIV latent infection. The model results suggest that although cell-to-cell transmission may have reduced susceptibility to HIV drugs, HIV latency represents a major reason for HIV persistence in patients on suppressive treatment.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Hui Liu, Chengfeng Sun, Fanwei Meng The 3D magneto-micropolar equations with damping are considered in this paper. We prove the existence and uniqueness of strong solution for 3D magneto-micropolar equations with damping for β≥4 with any α>0.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Alain Miranville, Ramón Quintanilla In this paper we consider the one-dimensional type III thermoelastic theory with voids. We prove that generically we have exponential stability of the solutions. This is a striking fact if one compares it with the behavior in the case of the thermoelastic theory based on the classical Fourier law for which the decay is generically slower.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Wenguang Cheng, Tianzhou Xu The truncated Painlevé expansion is used to obtain the residual symmetry of the combined KdV–negative-order KdV (KdV–nKdV) equation, which can be localized to the Lie point symmetry. The multiple residual symmetries are established and localized in the prolonged system by defining more new quantities, and the corresponding finite symmetry transformation which is nth Bäcklund transformation is given by determinant form. In addition, we derive a second order Lax pair by introducing a transformation. Finally, we apply the consistent Riccati expansion (CRE) method to prove that the combined KdV–nKdV equation is CRE solvable and construct exact interaction solution between the soliton and the cnoidal periodic wave.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Lucia Romani A C2 cubic local interpolating B2-spline, controllable by a shape parameter, is introduced and its properties are analyzed. An algorithm for the automatic selection of the free parameter is developed and tested on several examples. Finally, a two-phase subdivision scheme for its efficient evaluation at dyadic points is presented.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Chun-Yu Lei, Jia-Feng Liao In this paper, we devote ourselves to investigating a nonlocal problem involving singularity and asymptotically linear nonlinearities. By using the variational and perturbation methods, we obtain the existence of two positive solutions which improve the existing result in the literature.

Abstract: Publication date: August 2019Source: Applied Mathematics Letters, Volume 94Author(s): Teresa Faria, José J. Oliveira For the generalized periodic model of hematopoiesis x′(t)=−a(t)x(t)+∑i=1mbi(t)1+x(t−τi(t))n, with 0

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Pham Huu Anh Ngoc Using a novel approach, we present new explicit criteria for the mean square exponential stability of general non-linear stochastic differential equations. An application to stochastic neural networks is given.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Jinfeng Wang A reaction–diffusion equation coupled to an ODE on convex domains is proposed to model a single species with a non-mobile state and an active state. Under general cooperative/competitive interactions, a trivial stability on convex domains is shown and the reaction–diffusion–ODE system does not support interesting patterns.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Dongyang Shi, Yanmi Wu Uniform superconvergent analysis of a new low order nonconforming mixed finite element method (MFEM) is studied for solving the fourth order nonlinear Bi-wave singular perturbation problem (SPP) by EQ1rot element. On one hand, the existence, uniqueness and stability of the numerical solutions are proved. On the other hand, with the help of the special characters of this element, uniform superclose result of order O(h2) for the original variable in the broken H1 norm and uniform optimal order estimate of order O(h2) for the intermediate variable in L2 norm are deduced irrelevant to the real perturbation parameter δ appearing in the considered problem, respectively. In which, the nonlinear term in the Bi-wave SPP, which is the main difficulty in the whole error analysis, is dealt with rigorously through a novel splitting technique. Moreover, the global uniform superconvergent estimate is obtained with the interpolated postprocessing approach. Finally, some numerical results are provided to confirm the theoretical analysis. Here h is the subdivision parameter.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Xing Li, Li Xu, Hao Wang, Zhong-Hai Yang, Bin Li Based on an implicit time scheme, this paper presents a new implicit hybridizable discontinuous Galerkin time-domain (imHDGTD) method for solving the 3-D electromagnetic problems with locally refined meshes. Compared with the classical discontinuous Galerkin (DG) method, the proposed imHDGTD method has a larger suitable time step and the reduction in number of degrees of freedom (DOFs). Besides, we adopt the nodal hierarchical basis functions and further propose a matrix solving technology with an effective p-type multigrid preconditioner, which decreases significantly imHDGTD’s matrix factorization time and memory usage. Some numerical results show the accuracy and a higher computational performance of the imHDGTD, which illustrates this method more promising and effective for the complex multiscale electromagnetic problem.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Rong-Rong Jia, Rui Guo In this paper, we mainly study the (2+1)-dimensional Schrödinger–Maxwell–Blochequation (SMBE). We have constructed the generalized N-fold Darboux transformations (DT), and based on the plane wave solutions, the breather and rogue wave solutions are systematically generated, the dynamical features of those solutions are graphically represented.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Wenbin Gan, Shibo Liu In this paper, we study the existence of multiple positive solutions of Schrödinger–Poisson type equations with indefinite nonlinearity. Our main tool is the mountain pass theorem.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Weimin Han, Shengda Zeng Hemivariational inequalities have been successfully employed for mathematical and numerical studies of application problems involving nonsmooth, nonmonotone and multivalued relations. In recent years, error estimates have been derived for numerical solutions of hemivariational inequalities under additional solution regularity assumptions. Since the solution regularity properties have not been rigorously proved for hemivariational inequalities, it is important to explore the convergence of numerical solutions of hemivariational inequalities without assuming additional solution regularity. In this paper, we present a general convergence result enhancing existing results in the literature.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Tatyana Dobroserdova, Fuyou Liang, Grigory Panasenko, Yuri Vassilevski The paper introduces and compares several multiscale models of blood flow in the aortic bifurcation against a reference 3D FSI solution [1]. All these models reproduce the 3D flow in a small neighborhood of the junction. A three-scale model composed of 3D, 1D and 0D equations provides flow rate and pressure close to the reference 3D FSI solution.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Shuo Ma, Yanmei Kang The purpose of this paper is to present a periodic averaging method for impulsive stochastic differential equations with Lévy noise under non-Lipschitz condition. It is shown that the solutions of impulsive stochastic differential equations with Lévy noise converge to the solutions of the corresponding averaged stochastic differential equations without impulses

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Onur Baysal, Alemdar Hasanov In this study, solvability of the initial boundary value problem for general form Euler–Bernoulli beam equation which includes also moving point-loads is investigated. The complete proof of an existence and uniqueness properties of the weak solution of the considered equation with Dirichlet type boundary conditions is derived. The method used here is based on Galerkin approximation which is the main tool for the weak solution theory of linear evolution equations as well as in derivation of a priori estimate for the approximate solutions. All steps of the proposed technique are explained in detail.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Wenjing Xu, Wei Xu, Shuo Zhang This paper presents an averaging principle for Caputo fractional stochastic differential equations (FSDEs) driven by Brown motion. Under some assumptions, the solutions to FSDEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. The analyses of solutions to systems before and after averaging, allow to extend the classical Khasminskii approach to Caputo fractional stochastic equations.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Alexei Rybkin We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the solution is specified at an initial moment of time). We then show how our method applies in fluid mechanics. More specifically, we present a complete solution to the problem of long waves run-up in inclined bays of arbitrary shape with nonzero initial velocity.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Da-Wei Zuo, Gui-Fang Zhang Hirota equation has been studied in the past years, which can be used to describe the nonlinear waves in the fluids and nonlinear optical fibers. In this paper, nonlocal Hirota equations with the space (S)-, time (T)- and space–time (ST)-symmetry have been discussed. By virtue of the Hirota bilinear method, higher-order solutions of generalized Hirota equations have been obtained. As the special cases, exact solutions of the S-symmetric, T-symmetric and ST-symmetric nonlocal Hirota equations have been listed.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Ábel Garab, Mihály Pituk, Ioannis P. Stavroulakis It is well-known that for the oscillation of all solutions of the linear delay differential equation x′(t)+p(t)x(t−τ)=0,t≥t0, with p∈C([t0,∞),R+) and τ>0 it is necessary that B≔lim supt→∞A(t)≥1e,whereA(t)≔∫t−τtp(s)ds. Our main result shows that if the function A is slowly varying at infinity (in additive form), then under mild additional assumptions B>1e implies the oscillation of all solutions of the above linear delay differential equation. The applicability of the obtained results and the importance of the slowly varying assumption on A are illustrated by examples.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Jeffrey Uhlmann This paper identifies a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, it is shown that the conventional use of the Moore–Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. It is then shown that such properties can be rigorously preserved using an alternative generalized matrix inverse.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Xueke Pu, Ting Huang This paper proves a Wentzell–Freidlin type large deviation principle for the 2-D derivative Ginzburg–Landau equation perturbed by a small multiplicative noise, based on the Laplace principle and weak convergence approach.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Wei Zeng, Aiguo Xiao, Xueyang Li In this paper, we discuss the error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex space fractional Ginzburg-Landau equations. The continuous mass and energy inequalities as well as their discrete versions are presented. Moreover, by the discrete mass and energy inequalities, the error estimate of the Fourier pseudo-spectral scheme is established, and the scheme is proved to have the spectral accuracy.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Guanwei Chen, Martin Schechter In this paper, we obtain the existence of negative energy solutions for a class of non-periodic Schrödinger lattice systems with perturbed terms, where the nonlinearities are asymptotically-linear at infinity. In addition, an example is given to illustrate our results.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Qian-Min Huang Under investigation in this paper is the integrability and dark soliton solutions for a fifth-order variable coefficients nonlinear Schrödinger equation, which is used in an inhomogeneous optical fiber. Bilinear forms, Lax pair and infinitely-many conservation laws are obtained under an integrable constraint. Dark one-, two- and N-soliton solutions are constructed via the Hirota bilinear method.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Hui-Min Yin, Bo Tian, Cong-Cong Hu, Xin-Chao Zhao Perturbed nonlinear Schrödinger (NLS) equation with the power-law nonlinearity in a nano optical fiber is studied with the help of its equivalent two-dimensional planar dynamic system and Hamiltonian. Via the bifurcation theory and qualitative theory, equilibrium points for the two-dimensional planar dynamic system are obtained. With the external perturbation taken into consideration, chaotic motions for the perturbed NLS equation with the power-law nonlinearity are derived based on the equilibrium points.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Xiaofeng Zhang, Rong Yuan In this paper, based on the existing literature, we further study an important statistical character of a stochastic delayed chemostat model. By constructing suitable Lyapunov functional and using the stochastic Lyapunov analysis method, we investigate the existence of stationary distribution and the ergodicity of a stochastic delayed chemostat model, which can help us better understand the dynamic behavior and statistical characteristics of stochastic delayed biological models.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Yan Gu, Chia-Ming Fan, Rui-Ping Xu The traditional method of fundamental solutions (MFS) based on the “global” boundary discretization leads to dense and non-symmetric coefficient matrices that, although smaller in sizes, require huge computational cost to compute the system of equations using direct solvers. In this study, a localized version of the MFS (LMFS) is proposed for the large-scale modeling of two-dimensional (2D) elasticity problems. In the LMFS, the whole analyzed domain can be divided into small subdomains with a simple geometry. To each of the subdomain, the traditional MFS formulation is applied and the unknown coefficients on the local geometric boundary can be calculated by the moving least square method. The new method yields a sparse and banded matrix system which makes the method very attractive for large-scale simulations. Numerical examples with up to 200,000 unknowns are solved successfully using the developed LMFS code.

Abstract: Publication date: July 2019Source: Applied Mathematics Letters, Volume 93Author(s): Weihong Xie, Haibo Chen This paper is concerned with the following Kirchhoff type problems (0.1)−(a+b∫Ω ∇u 2dx)Δu=λ u q−2u+ u p−2u,x∈Ω,u=0,x∈∂Ω,where constants a,b>0, the parameter λ≥0, 1

Abstract: Publication date: Available online 22 March 2019Source: Applied Mathematics LettersAuthor(s): Bendong Lou The so-called zero number diminishing property (or zero number argument) is a powerful tool in qualitative studies of one dimensional parabolic equations, which says that, under the zero- or non-zero-Dirichlet boundary conditions, the number of zeroes of the solution u(x,t) of a linear equation is finite, non-increasing and strictly decreasing when there are multiple zeroes (cf. Angenent (1988)). In this paper we extend the result to the problems with more general boundary conditions: u=0 sometime and u≠0 at other times on the domain boundaries. Such results can be applied in particular to parabolic equations with Robin and free boundary conditions.

Abstract: Publication date: Available online 22 March 2019Source: Applied Mathematics LettersAuthor(s): Yongxiang Li, Yabing Gao This paper deals with the solvability of the fourth-order boundary value problem u(4)=f(x,u,u′′),0≤x≤1,u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. Inequality conditions on f guaranteeing the existence and uniqueness of solution are presented. The inequality conditions allow that f(x,u,v) may be superlinear growth on u and v as (u,v) →∞.

Abstract: Publication date: Available online 20 March 2019Source: Applied Mathematics LettersAuthor(s): Dumitru Motreanu, Patrick Winkert The existence of solutions of opposite constant sign is proved for a Dirichlet problem driven by the weighted (p,q)-Laplacian with q

Abstract: Publication date: Available online 20 March 2019Source: Applied Mathematics LettersAuthor(s): Thomas Trogdon Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the matrix–vector product with an N-dimensional vector can be performed in O(NlogN) operations. In the simplest situation, these random matrices coincide with Haar measure on a subgroup of the orthogonal group. We discuss other implications in the context of randomized linear algebra.

Abstract: Publication date: Available online 19 March 2019Source: Applied Mathematics LettersAuthor(s): Yan-bo Hu, Yun-guang Lu, Naoki Tsuge In this paper, we apply the viscosity-flux approximation method coupled with the maximum principle to obtain the a-priori L∞ estimates for the approximation solutions of the compressible polytropic gas dynamics system with an outer force, and prove the global existence of entropy solutions for any adiabatic exponent γ>1.The present problem was classical and the global existence was known long ago. However, the L∞ estimates grow larger with respect to the time variable. As a result, it does not guarantee the stability of solutions. We thus prove the uniformly L∞ estimate with respect to the time variable. This means that our solutions are stable. The key idea is to employ an invariant region depending on the space and time variables. This method enable us to investigate the behavior of solutions in detail and deduce the desired estimates.

Abstract: Publication date: Available online 19 March 2019Source: Applied Mathematics LettersAuthor(s): Xinhe Wang, Zhen Wang, Hao Shen In this letter, a discrete SIS (susceptible-infected-susceptible) epidemic model on complex networks is presented. Firstly, the non-negativity and the boundedness of solutions are studied. Secondly, the basic reproduction number R0 is calculated. Thirdly, applying the Lyapunov direct method of difference equations, the global asymptotic stability of disease free equilibrium is investigated. Finally, there gives some simulations.

Abstract: Publication date: Available online 19 March 2019Source: Applied Mathematics LettersAuthor(s): Vincenzo Ambrosio, Teresa Isernia In this note we improve the recent results established in Ambrosio and Isernia (2018) concerning the multiplicity and concentration of positive solutions for the following class of p-fractional Schrödinger equations: εsp(−Δ)psu+V(x) u p−2u=f(u)+γ u ps∗−2uinRN,where ε>0, s∈(0,1), p∈(1,∞), N>sp, γ∈{0,1}, ps∗=NpN−sp is the fractional critical exponent, (−Δ)ps is the fractional p-Laplacian operator, V is a continuous positive potential satisfying the Rabinowitz condition (Rabinowitz, 1992), and f is a superlinear continuous function with subcritical growth at infinity. Here we do not assume the well-known Ambrosetti–Rabinowitz condition (Ambrosetti and Rabinowitz, 1973) on f and we complete the study in the critical case γ=1.

Abstract: Publication date: Available online 19 March 2019Source: Applied Mathematics LettersAuthor(s): Chuan–Yun Gu, Jun Zhang, Guo–Cheng Wu A new class of fractional differential equations with the Riesz–Caputo derivative is proposed and the physical meaning is introduced in this paper. The boundary value problem is investigated under some conditions. Leray–Schauder and Krasnoselskii’s fixed point theorems in a cone are adopted. Existence of positive solutions is provided. Finally, two examples with numerical solutions are given to support theoretical results.

Abstract: Publication date: Available online 18 March 2019Source: Applied Mathematics LettersAuthor(s): V. Bobkov, P. Drábek, Y. Ilyasov We show that the elliptic equation with non-Lipschitz right-hand side, −Δu=λ u β−1u− u α−1u with λ>0 and 0

Abstract: Publication date: Available online 18 March 2019Source: Applied Mathematics LettersAuthor(s): Shuyan Chen, Zhenya Yan The matrix Riemann-Hilbert problem of the Hirota equation with non-zero boundary conditions is investigated. Based on the matrix Riemann-Hilbert problem, the n-fold Darboux transformation is established for the Hirota equation such that (2n−1,2n)th-order rogue waves can be found simultaneously. Particularly, we exhibit the first-, second-, third-, and fourth-order rogue waves, and first- and second-order temporal-spatial and spatial periodic breathers for some parameters, respectively.

Abstract: Publication date: Available online 15 March 2019Source: Applied Mathematics LettersAuthor(s): Xinwei Wang, Zhangxian Yuan A comparison is made of the finite differences as a sum-accelerated pseudospectral method (FDSPM) and the discrete singular convolution (DSC) algorithms in free vibration analysis for the first time. Taylor series expansion method is used to eliminate the friction points. Some important issues on these numerical methods are addressed from the practical application point of view.

Abstract: Publication date: Available online 15 March 2019Source: Applied Mathematics LettersAuthor(s): Shihu Li, Wei Liu, Yingchao Xie In this work we establish the exponential mixing property for stochastic 3D fractional Leray-α model with degenerate noise. The main result is also applicable to stochastic 3D hyperviscous Navier–Stokes equations and stochastic 3D critical Leray-α model.

Abstract: Publication date: Available online 14 March 2019Source: Applied Mathematics LettersAuthor(s): Xiangcheng Zheng, Hong Wang We prove the wellposedness of a nonlinear variable-order fractional wave differential equation that describes the vibration of a single particle attached to a viscoelastic material. We then prove that the high-order regularity of its solution depends on the behavior of the variable orders α(t) and β(t) of the fractional damping terms at t=0. In particular, we prove that the solution to the model recovers full regularity when the fractional damping terms exhibit (the physically relevant) elastic restoration force and integer-order damping at the initial time t=0, which, thus, eliminates the incompatibility between the nonlocal differential operators and the locality of classical initial condition.

Abstract: Publication date: Available online 13 March 2019Source: Applied Mathematics LettersAuthor(s): Junyuan Yang, Zhen Jin, Fei Xu An SIR epidemic model with age-since-infection and diffusion is proposed. The next generation operator R has been explicitly calculated by a renewal process. The basic reproduction number R0 is defined by the spectral radius of R. The system exhibits a sharp threshold dynamics in terms of R0.