Authors:Jaume Giné; Jaume Llibre Pages: 130 - 131 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Jaume Giné, Jaume Llibre We study the local analytic integrability for real Liénard systems, x ̇ = y − F ( x ) , y ̇ = x , with F ( 0 ) = 0 but F ′ ( 0 ) ≠ 0 , which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [ p : − q ] resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the [ p : − q ] resonant saddle into a strong saddle.

Authors:Zhang Daoxiang; Ping Yan Pages: 1 - 5 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Zhang Daoxiang, Ping Yan In this paper we consider a predator–prey model with Leslie–Gower functional response. We present the necessary and sufficient conditions for the nonexistence of limit cycles by the application of the generalized Dulac theorem. As a result, we give the necessary and sufficient conditions for which the local asymptotic stability of the positive equilibrium implies the global stability for this model. Our results extend and improve the results presented by Aghajani and Moradifam (2006) and Hsu and Huang (1995).

Authors:Gabriela Holubová; Jakub Janoušek Pages: 6 - 13 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Gabriela Holubová, Jakub Janoušek This paper brings a revision of the so far known uniqueness result for a one-dimensional damped model of a suspension bridge. Using standard techniques, however with finer arguments, we provide a significant improvement and extension of the allowed interval for the stiffness parameter.

Authors:Mengwu Guo; Hongzhi Zhong Pages: 14 - 23 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Mengwu Guo, Hongzhi Zhong On the basis of the dual variational formulation of a class of elliptic variational inequalities, a constitutive relation error is defined for the variational inequalities as an a posteriori error estimator, which is shown to guarantee strict upper bounds of the global energy-norm errors of kinematically admissible solutions. A numerical example is presented to validate the strictly bounding property of the constitutive relation error for the variational inequalities in question.

Authors:Shugui Kang Pages: 24 - 29 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Shugui Kang We study the existence and the uniqueness of positive periodic solutions for a class of integral equationsof the form ϕ ( x ) = ∫ [ x , x + ω ] ∩ G K ( x , y ) [ f 1 ( y , ϕ ( y − τ ( y ) ) ) + f 2 ( y , ϕ ( y − τ ( y ) ) ) ] d y , x ∈ G , where G is a closed subset of R N with periodic structure. Our analysis relies on the fixed point theory for mixed monotone operator in Banach space.

Authors:John A.D. Appleby; Denis D. Patterson Pages: 30 - 37 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): John A.D. Appleby, Denis D. Patterson In this letter, we obtain sharp estimates on the growth rate of solutions to a nonlinear ODE with a nonautonomous forcing term. The equation is superlinear in the state variable and hence solutions exhibit rapid growth and finite-time blow-up. The importance of ODEs of the type considered here stems from the key role they play in understanding the asymptotic behaviour of more complex systems involving delay and randomness.

Authors:Ferenc Izsák; Béla J. Szekeres Pages: 38 - 43 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Ferenc Izsák, Béla J. Szekeres Space-fractional diffusion problems are investigated from the modeling point of view. It is pointed out that the elementwise power of the Laplacian operator in R n is an inadequate model of fractional diffusion. Also, the approach with fractional calculus using zero extension is not a proper model of homogeneous Dirichlet boundary conditions. At the time, the spectral definition of the fractional Dirichlet Laplacian seems to be in many aspects a proper model of fractional diffusion.

Authors:Sunho Choi; Jaywan Chung; Yong-Jung Kim Pages: 51 - 58 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Sunho Choi, Jaywan Chung, Yong-Jung Kim Inviscid traveling waves are ghost-like phenomena that do not appear in reality because of their instability. However, they are the reason for the complexity of the traveling wave theory of reaction–diffusion equations and understanding them will help to resolve related puzzles. In this article, we obtain the existence, the uniqueness and the regularity of inviscid traveling waves under a general monostable nonlinearity that includes non-Lipschitz continuous reaction terms. Solution structures are obtained such as the thickness of the tail and the free boundaries.

Authors:Xin Jiang; Gang Meng; Zhikun She Pages: 59 - 66 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Xin Jiang, Gang Meng, Zhikun She In this paper, we investigate the existence of positive T -periodic solutions in a food web with one predator feeding on n preys by Leray–Schauder degree theory, which plays a significant role on further studying the uniqueness of limit cycles of this food web model. We start with a series of required spaces and operators and construct a bounded open set Ω over which the corresponding Leray–Schauder degree can be well-defined. Afterwards, by the invariance property of homotopy, we verify that the Leray–Schauder degree is not equal to 0 under certain conditions, thus implying the existence of positive T -periodic solutions. Finally, a numerical example is presented to illustrate our result.

Authors:Tieshan He; Yehui Huang; Kaihao Liang; Youfa Lei Pages: 67 - 73 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Tieshan He, Yehui Huang, Kaihao Liang, Youfa Lei We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator and an indefinite potential. Using variational methods together with flow invariance arguments, we show that the problem has at least one nodal solution. The result presented in this paper gives an answer to the open question raised by Papageorgiou and Rădulescu (2016).

Authors:Toka Diagana Pages: 74 - 80 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Toka Diagana In this paper we study the well-posedness for some damped elastic systems in a Banach space. To illustrate our abstract results, we study the existence of classical solutions to some elastic systems with viscous and strong dampings.

Authors:Abdul-Majid Wazwaz Pages: 1 - 6 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Abdul-Majid Wazwaz In this work we establish a two-mode modified Korteweg–de Vries equation (TmKdV). We show that multiple soliton solutions exist for specific values of the nonlinearity and dispersion parameters of this equation. We also derive more exact solutions for other values of these parameters. We will use the simplified Hirota’s method, the tanh/coth method to conduct this analysis.

Authors:Andrea N. Ceretani; Natalia N. Salva; Domingo A. Tarzia Pages: 14 - 17 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Andrea N. Ceretani, Natalia N. Salva, Domingo A. Tarzia This article is devoted to the proof of the existence and uniqueness of the modified error function introduced in Cho and Sunderland (1974). This function is defined as the solution to a nonlinear second order differential problem depending on a real parameter. We prove here that this problem has a unique non-negative analytic solution when the parameter assumes small positive values.

Authors:M.C. Leseduarte; R. Quintanilla; R. Racke Pages: 18 - 25 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): M.C. Leseduarte, R. Quintanilla, R. Racke We study solutions for the one-dimensional problem of the Green–Lindsay and the Lord–Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green–Lindsay model, but the non-exponential stability for the Lord–Shulman model.

Authors:Zhongli Liu Pages: 26 - 31 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Zhongli Liu In this paper, we provide a criterion on the axial equilibrium to be globally asymptotically stable for the n -dimensional Gompertz system, i.e., only one species will survive and stabilize at its own carrying capacity, whilst all the other species are driven to extinction.

Authors:Juan Huang; Jian Zhang Pages: 32 - 38 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Juan Huang, Jian Zhang This paper concerns the exact value of cross-constrain problem and strong instability of standing waves in trapped dipolar quantum gases. By analyzing the characters of ground state, we give the relation of the cross-constrain problem and constrain problems. Then the exact value of the cross-constrain problem is obtained in the form of the ground state which is relevant to the frequency. Finally, we show the standing waves are strongly unstable.

Authors:Ying Xie; Chengjian Zhang Pages: 46 - 51 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Ying Xie, Chengjian Zhang This paper deals with nonlinear stochastic neutral differential equations (SNDEs) with time-variable delay and markovian switching. Several criteria for asymptotical boundedness and moment exponential stability of the equations are derived. An example is given to illustrate the criteria.

Authors:Ting Li; Fengqin Zhang; Hanwu Liu; Yuming Chen Pages: 52 - 57 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Ting Li, Fengqin Zhang, Hanwu Liu, Yuming Chen In this paper, we propose an SIRS epidemic model with a nonlinear incidence and transfer from infectious to susceptible. Applying LaSalle’s invariance principle and Lyapunov direct method, we establish a threshold dynamics completely determined by the basic reproduction number.

Authors:Chao Wang; Ravi P. Agarwal Pages: 58 - 65 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Chao Wang, Ravi P. Agarwal In this paper, we propose two new concepts of mean-square almost periodic stochastic process based on a new concept of periodic time scales introduced by Adıvar (2013). Then we provide some sufficient conditions to guarantee the existence of mean-square almost periodic solution for a new type of neutral impulsive stochastic Lasota–Wazewska model involving q -difference model on time scales.

Authors:Yu Zhu; Meng Liu Pages: 1 - 7 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Yu Zhu, Meng Liu In this paper, a stochastic service–resource mutualism model is proposed and studied. For each species, the threshold between stochastic permanence and extinction is established. The effects of stochastic perturbations on the permanence and extinction of the resource species and the service species are revealed.

Authors:Fang-Fang Liao Pages: 8 - 14 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Fang-Fang Liao We study the existence of positive periodic solutions for a second order differential equation which is related to the Liebau phenomenon. The proof is based on the fixed point theorem in cones. Our results improve and generalize those in the literature.

Authors:Zhijian Yang; Zhiming Liu Pages: 22 - 28 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Zhijian Yang, Zhiming Liu The paper investigates the upper semicontinuity of global attractors A α of a family of semilinear wave equations with gentle dissipation: u t t − △ u + γ ( − △ ) α u t + f ( u ) = g ( x ) , with α ∈ ( 0 , 1 ∕ 2 ) . It is a continuation of researches in Yang et al. (2016), where the existence of global attractors of the equations has been established. We further show that for any neighborhood U of A α 0 , α 0 ∈ ( 0 , 1 ∕ 2 ) , A α ⊂ U when 0 < α − α 0 ≪ 1 .

Authors:Nikolay A. Kudryashov Pages: 29 - 34 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Nikolay A. Kudryashov Continuum model corresponding to the generalization of both the Fermi–Pasta–Ulam and the Frenkel–Kontorova models is considered. This generalized model can be used for the description of nonlinear dislocation waves in the crystal lattice. Using the Painlevé test we analyze the integrability of this equation. We find that there exists an integrable case of the partial differential equation for nonlinear dislocations. Exact solutions of nonlinear dislocation equation are presented.

Authors:Yuchan Wang; Jijun Liu Pages: 42 - 48 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Yuchan Wang, Jijun Liu When electronic devices are in operation, the sharp change of the temperature on devices surface can be considered as an indicator of devices faults. Based on this engineering background, we consider an inverse problem for 1-dimensional heat conduction model, with the aim of detecting the nonsmooth heat dissipation coefficient from measurable temperature on the device surface. We establish the uniqueness for the nonsmooth dissipation coefficient and prove the convergence property of the minimizer of the regularizing cost functional for the inverse problem theoretically. Then a double-iteration scheme minimizing the data-match term and the regularization term alternatively is proposed to implement the reconstructions.

Authors:Lixing Han Pages: 49 - 54 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Lixing Han Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive solution to a multilinear system with a nonsingular M-tensor and a positive right side vector. We analyze the method and prove its convergence to the desired solution. We report some numerical results based on an implementation of the proposed method using a prediction–correction approach for path following.

Authors:Liangwei Wang Pages: 55 - 60 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Liangwei Wang In this paper, we consider the Cauchy problem of the evolution p -Laplacian equation, and reveal the fact that there exists an equivalence relation between the ω -limit set of solutions and the ω -limit set of initial values. This relation can be used to prove different asymptotic behaviors of solutions, and two examples are given at the end of this paper.

Authors:Xiaowei Liu; Jin Zhang Pages: 61 - 66 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Xiaowei Liu, Jin Zhang In this paper we analyze a streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection diffusion problem. By decreasing the standard stabilization parameter properly near the exponential layers, we obtain uniform estimates in a new norm which is stronger than the usual ε -energy norm and weaker than the standard streamline diffusion norm. Through the analysis we know about the influences of the stabilization parameter on the SDFEM solutions.

Authors:Lifang Pei; Dongyang Shi Pages: 67 - 74 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Lifang Pei, Dongyang Shi A nonconforming finite element method (FEM for short) is proposed and analyzed for a plate contact problem by employing the Bergan’s energy-orthogonal plate element. Because the shape function and its first derivatives of this element are discontinuous at the element’s vertices, which is quite different from the conventional finite elements used in the existing literature, some novel approaches, including interpolation operator splitting and energy orthogonality, are developed to present a new error analysis for deriving an optimal estimate of order O ( h ) . At last, some numerical results are also provided to confirm the theoretical analysis.

Authors:Vo Anh Khoa; Tran The Hung Pages: 75 - 81 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Vo Anh Khoa, Tran The Hung This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit its importance to engineering circumstances. Therefore, coping with that impediment helps us improve the use of some regularization methods in real-world applications. This work also considers the presence of the power-law nonlinearities.

Authors:Xiaowei An; Xianfa Song Pages: 82 - 86 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Xiaowei An, Xianfa Song In this paper, using a delicate application of general Sobolev inequality, we establish the lower bound for the blowup time of the solution to a quasi-linear parabolic problem, which improves the result of Theorem 2.1 in Bao and Song (2014).

Authors:Chunhong Zhang; Zhisu Liu Pages: 87 - 93 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Chunhong Zhang, Zhisu Liu In this paper, we study the following Kirchhoff type problem with critical growth − M ∫ Ω ∇ u 2 d x △ u = λ u 2 u + u 4 u in Ω , u = 0 on ∂ Ω , where Ω is a smooth bounded domain in R 3 , M ∈ C ( R + , R ) and λ > 0 . We prove the existence of multiple nontrivial solutions for the above problem, when parameter λ belongs to some left neighborhood of the eigenvalue of the nonlinear operator − M ( ∫ Ω ∇ u 2 d x ) △ .

Authors:Huanying Xu; Xiaoyun Jiang; Bo Yu Pages: 94 - 100 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Huanying Xu, Xiaoyun Jiang, Bo Yu This work numerically investigates the space fractional Navier–Stokes equations obtained through replacing Laplacian operator in Navier–Stokes equations by Riesz fractional derivatives. The pressure-driven flow between two parallel plates is solved with the finite difference method of fractional differential equations. The influence of pertinent parameters on the characteristics of fluid flow is analyzed with graphics. Further, the Levenberg–Marquardt algorithm is also proposed to estimate model parameters.

Authors:Hai-Qiang Zhang; Rui Hu; Meng-Yue Zhang Pages: 101 - 105 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Hai-Qiang Zhang, Rui Hu, Meng-Yue Zhang In this Letter, the Darboux transformation is first applied to the defocusing Sasa–Satsuma equation which describes the propagation dynamics of ultrashort light pulses in the normal dispersion regime of optical fibers. The N -fold iterative transformation is expressed in terms of the determinants. This transformation enables us to construct explicit analytical dark soliton solutions from non-vanishing background. In illustration, the single-dark soliton solution is presented from the once-iterated formula.

Authors:Yuri Kondratiev; Yuri Kozitsky Pages: 106 - 112 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Yuri Kondratiev, Yuri Kozitsky The Markov dynamics is studied of an infinite system of point entities placed in R d , in which the constituents disperse and die, also due to competition. Assuming that the dispersal and competition kernels are continuous and integrable we show that the evolution of states of this model preserves their sub-Poissonicity, and hence the local self-regulation (suppression of clustering) takes place. Upper bounds for the correlation functions of all orders are also obtained for both long and short dispersals, and for all values of the intrinsic mortality rate.

Authors:Guoqiang Zhang; Zhenya Yan; Yong Chen Pages: 113 - 120 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Guoqiang Zhang, Zhenya Yan, Yong Chen We investigate the defocusing integrable nonlocal nonlinear Schrödinger (nNLS) equation using the loop group method and perturbation expansion idea. The associated N -fold Darboux transformation is presented in terms of the simple determinants. As the application of the N -fold Darboux transformation, we find the higher-order rational solitons of the nNLS equation, which exhibit many new types of soliton structures. Moreover, we also numerically study the stability of some rational solitons. The results are useful to explain the corresponding wave phenomena in nonlocal wave models.

Authors:Stylianos Dimas; Igor Leite Freire Pages: 121 - 125 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Stylianos Dimas, Igor Leite Freire We study a family of PDEs, which was derived as an approximation of an extended Lotka–Volterra system, from the point of view of symmetries. Also, by performing the self adjoint classification on that family we offer special cases possessing non trivial conservation laws. Using both classifications we justify the particular cases studied in the literature, and we give additional cases that may be of importance.

Authors:Jozef Džurina; Irena Jadlovská Pages: 126 - 132 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Jozef Džurina, Irena Jadlovská The purpose of this paper is to study the second-order half-linear delay differential equation r ( t ) y ′ ( t ) α ′ + q ( t ) y α ( τ ( t ) ) = 0 under the condition ∫ ∞ r − 1 ∕ α ( t ) d t < ∞ . Contrary to most existing results, oscillation of the studied equation is attained via only one condition. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.

Authors:Marc Bakry Pages: 133 - 137 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Marc Bakry We construct a reliable goal-oriented a posteriori error estimate for the oscillating single layer equation in acoustics. It is based on the computation of the residual corresponding to the primal problem and a reconstruction of the local error for the solution of the dual problem following the Dual-Weighted-Residual approach. We give a numerical example in 2D where the target is the far field value in some direction.

Authors:Aymen Laadhari Pages: 138 - 145 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Aymen Laadhari In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial computational savings. A suitable transformation avoids the introduction of an additional mixed variable in the variational problem. An exact tangent problem is derived and the nonlinear problem is solved by a quadratically convergent Newton method. In addition, we consider a generalization to the multidimensional case of the Kou’s and McDougall’s methods, resulting in a faster convergence. The method is benchmarked against known results with the aim of illustrating its accuracy and robustness.

Authors:Bérangère Delourme; Patrick Joly; Elizaveta Vasilevskaya Pages: 146 - 152 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Bérangère Delourme, Patrick Joly, Elizaveta Vasilevskaya In this note, we exhibit a three dimensional structure that permits to guide waves. This structure is obtained by a geometrical perturbation of a 3D periodic domain that consists of a three dimensional grating of equi-spaced thin pipes oriented along three orthogonal directions. Homogeneous Neumann boundary conditions are imposed on the boundary of the domain. The diameter of the section of the pipes, of order ε > 0 , is supposed to be small. We prove that, for ε small enough, shrinking the section of one line of the grating by a factor of μ ( 0 < μ < 1 ) creates guided modes that propagate along the perturbed line. Our result relies on the asymptotic analysis (with respect to ε ) of the spectrum of the Laplace–Neumann operator in this structure. Indeed, as ε tends to 0 , the domain tends to a periodic graph, and the spectrum of the associated limit operator can be computed explicitly.

Authors:Jae-Myoung Kim Pages: 153 - 160 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Jae-Myoung Kim We give a weak − L p Serrin type regularity criteria of weak solutions to the 3D viscoelastic Navier–Stokes equations with damping, which is described as an incompressible non-Newtonian fluid in the whole space R 3 .

Authors:Hui Wang; Yun-Hu Wang Pages: 161 - 167 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Hui Wang, Yun-Hu Wang By using the truncated Painlevé expansion and consistent Riccati expansion (CRE), we investigate a dissipative ( 2 + 1 )-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) equation. Through the truncated Painlevé expansion, its nonlocal symmetry and Bäcklund transformation (BT) are presented. Then the nonlocal symmetry is localized to the corresponding nonlocal group by an enlarged system. Based on the CRE method proposed by Lou (2013), the AKNS equation is proved CRE solvable, and the soliton-cnoidal wave interaction solutions are explicitly given.

Authors:Song Liu; Xiang Wu; Yan-Jie Zhang; Ran Yang Pages: 168 - 173 Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Song Liu, Xiang Wu, Yan-Jie Zhang, Ran Yang In this paper, the asymptotical stability of Riemann–Liouville fractional neutral systems is investigated. Applying Lyapunov direct method, we present new sufficient conditions on asymptotical stability in terms of linear matrix inequality (LMI) which can be easily solved. The advantage of our employed method is that one may directly calculate integer-order derivatives of the Lyapunov functions. Finally, two simple examples are given to show that the proposed method is computationally flexible and efficient.

Authors:Lei Qiao Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Lei Qiao Let a ( X , y ) be a nonnegative radical potential in a cylinder. In this paper, we study the solutions of the Dirichlet–Sch problem associated with a stationary Schrödinger operator. Existence of solutions for the Schrödinger equation and asymptotic properties as y → + ∞ and y → − ∞ are also considered under suitable conditions.

Authors:Fatma Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Fatma Karakoç We investigate oscillation about the positive equilibrium point of a population model with piecewise constant argument. By using linearized oscillation theory for difference equations a necessary and sufficient condition for the oscillation is obtained. Moreover it is showed that every nonoscillatory solution approaches to the equilibrium point as t tends to infinity.

Authors:Ting Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Ting Su A Modified 2+1-Dimensional Coupled Burgers equation and its Lax pairs are proposed. A Darboux transformation for the Modified 2+1-Dimensional Coupled Burgers equation and its Lax pairs is established with the help of the gauge transformation between spectral problems. As an application of the Darboux transformation, we give some explicit solutions of the Modified 2+1-Dimensional Coupled Burgers equation.

Authors:Kai Liu Abstract: Publication date: July 2017 Source:Applied Mathematics Letters, Volume 69 Author(s): Kai Liu In this note, we shall consider the norm continuity of a class of solution semigroups associated with linear functional differential equations of neutral type with time lag r > 0 in Hilbert spaces. The norm continuity plays an important role in the analysis of asymptotic stability of the system under consideration by means of spectrum approaches. We shall show that for a square integrable neutral delay term and an unbounded infinitesimal generator A multiplied by a square integrable weight function in the distributed delay term, the associated solution semigroup of the system is norm continuous at every t > r .