Authors:Junfeng LIU; Ciprian A. TUDOR Pages: 1545 - 1566 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Junfeng LIU, Ciprian A. TUDOR In this paper we study a fractional stochastic heat equation on R d ( d ≥ 1 ) with additive noise ∂ ∂ t u ( t , x ) = d δ _ α _ u ( t , x ) + b ( u ( t , x ) ) + W ˙ H ( t , x ) where d δ _ α _ is a nonlocal fractional differential operator and W ˙ H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d=1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.

Authors:Samir KALLEL Pages: 1567 - 1593 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Samir KALLEL The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces Λ α , p , q k ( R ) , α ∈ R and 1 ≤ p , q ≤ ∞ , in the context of Dunkl harmonic analysis.

Authors:Yanli HAN; Yan GAO Pages: 1594 - 1606 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Yanli HAN, Yan GAO This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points (extreme points) and the existing ones need to verify all points in the bounded polyhedron.

Authors:Xiang GAO; Jihua MA Pages: 1607 - 1618 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Xiang GAO, Jihua MA This paper is concerned with the Diophantine properties of the sequence { ξ θ n } , where 1 ≤ ξ < θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μ λ with λ = θ - 1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μ λ almost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

Authors:Zi WANG; Yuwen WANG Pages: 1619 - 1631 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Zi WANG, Yuwen WANG In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is “the generalized Neumann lemma” which is quite different from the method in [12] where “the generalized Banach lemma” was used. By the method of the perturbation analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.

Authors:Zhensheng GAO; Zhong TAN Pages: 1632 - 1638 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Zhensheng GAO, Zhong TAN In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in R 3 . We establish a criterion for possible breakdown of such solutions at a finite time. More precisely, if (u,d) is smooth up to time T provided that ∫ 0 T ∇ × u ( t , ⋅ ) B M O ( R 3 ) + ∇ d ( t , ⋅ ) L 4 ( R 3 ) 8 d t < ∞ .

Authors:Hua CHEN; Hongge CHEN; Yirui DUAN; Xin HU Pages: 1653 - 1664 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Hua CHEN, Hongge CHEN, Yirui DUAN, Xin HU Let Ω be a bounded open domain in R n with smooth boundary ∂Ω, X = ( X 1 , X 2 , ⋯ , X m ) be a system of real smooth vector fields defined on Ω and the boundary ∂Ω is non-characteristic for X. If X satisfies the Hörmander's condition, then the vector field is finitely degenerate and the sum of square operator Δ X = ∑ j = 1 m X j 2 is a finitely degenerate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators ΔX on Ω.

Authors:Zhiying DENG; Yisheng HUANG Pages: 1665 - 1684 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Zhiying DENG, Yisheng HUANG This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in R N . By virtue of variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions.

Authors:Lingyun GAO; Manli LIU Pages: 1685 - 1694 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Lingyun GAO, Manli LIU By use of Nevanlinna value distribution theory, we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation, the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth.

Authors:Jongrak LEE Pages: 1695 - 1704 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Jongrak LEE In this paper we consider the block Toeplitz operators T Phi on the weighted Bergman space A α 2 ( D , C n ) and we give a necessary and sufficient condition for the hyponormality of block Toeplitz operators with symbol in the class of functions Φ = F + G * with matrix-valued polynomial functions F and G with degree 2.

Authors:Suiming SHANG; Yu TIAN; Yajing ZHANG Pages: 1705 - 1726 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Suiming SHANG, Yu TIAN, Yajing ZHANG In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.

Authors:Iz-iddine EL-FASSI; Janusz BRZDĘK; Abdellatif CHAHBI; Samir KABBAJ Pages: 1727 - 1739 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Iz-iddine EL-FASSI, Janusz BRZDĘK, Abdellatif CHAHBI, Samir KABBAJ We present results on approximate solutions to the biadditive equation f ( x + y , z - w ) + f ( x - y , z + w ) = 2 f ( x , z ) - 2 f ( y , w ) on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.

Authors:Tianyuan XU; Chunhua JIN; Shanming JI Pages: 1740 - 1760 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Tianyuan XU, Chunhua JIN, Shanming JI This paper deals with the existence and the asymptotic behavior of discontinuous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonlinear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena.

Authors:Dinghuai WANG; Jiang ZHOU; Wenyi CHEN Pages: 1761 - 1774 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Dinghuai WANG, Jiang ZHOU, Wenyi CHEN This manuscript addresses Muckenhoupt A p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A p class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L p(ω) to weighted Morrey spaces M q p ( ω ) for 1 < q < p < ∞. As a corollary, if M is (weak) bounded on M q p ( ω ) , then ω ∈ A p. The A p condition also characterizes the boundedness of the Riesz transform R j and convolution operators T ɛ on weighted Morrey spaces. Finally, we show that ω ∈ A p if and only if ω ∈ B M O p ′ ( ω ) for 1 ≤ p < ∞ and 1/p+1/p′=1.

Authors:Lijuan WANG Pages: 1775 - 1790 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Lijuan WANG The large time behavior of solutions to the two-dimensional perturbed Hasegawa-Mima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green function, we not only obtain the optimal decay rate but also establish the pointwise estimate of global classical solutions.

Authors:Shenlian LI; Xuejun ZHANG; Si XU Pages: 1791 - 1802 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Shenlian LI, Xuejun ZHANG, Si XU Let Ω be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p,q,s) on Ω. Characterizing functions in the F(p,q,s) space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F(p,q,s) space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F(p,q,s) space and Bloch type space on Ω too.

Authors:Fanchao KONG; Zhiguo LUO Pages: 1803 - 1816 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Fanchao KONG, Zhiguo LUO This paper is concerned with the non-Newtonian filtration equations with nonlinear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

Authors:Yanyan CUI; Chaojun WANG; Hao LIU Pages: 1817 - 1829 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Yanyan CUI, Chaojun WANG, Hao LIU In this paper, we extend the Roper-Suffridge extension operator in complex Banach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit ball in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spirallike mappings in several complex variables.

Authors:Shuangting LAN; Zongxuan CHEN Pages: 1830 - 1840 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Shuangting LAN, Zongxuan CHEN In this paper, we investigate difference Painlevé IV equations, and obtain some results on Nevanlinna exceptional values of transcendental meromorphic solutions w(z) with finite order, their differences Δ w ( z ) = w ( z + 1 ) - w ( z ) and divided differences Δ w ( z ) w ( z ) .

Authors:Rong DONG; Dongsheng LI Pages: 1841 - 1860 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Rong DONG, Dongsheng LI In this paper, a type of nonlinear elliptic equations with rapidly oscillatory coefficients is investigated. By compactness methods, we show uniform Hölder estimates of solutions in a C 1 bounded domain.

Authors:Daochun SUN; Yingying HUO; Yinying KONG; Fujie CHAI Pages: 1861 - 1869 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Daochun SUN, Yingying HUO, Yinying KONG, Fujie CHAI In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

Authors:Quanqing LI; Xian WU Pages: 1870 - 1880 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Quanqing LI, Xian WU In this paper, we study the following generalized quasilinear Schrödinger equations with critical or supercritical growths - div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) ∇ u 2 + V ( x ) u = f ( x , u ) + λ u p - 2 u , x ∈ R N , where λ > 0 , N ≥ 3 , g : R → R + is a C 1 even function, g ( 0 ) = 1 , g ′ ( s ) ≥ 0 for all s ≥ 0 , lim s → + ∞ g ( s ) s α - 1 : β > 0 for some α ≥ 1 and ( α - 1 ) g ( s ) > g ′ ( s ) s for all s > 0 and p ≥ α2*. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 using a change of variables and variational method.

Authors:Hakho HONG; Teng WANG Pages: 1177 - 1208 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Hakho HONG, Teng WANG For the general gas including ideal polytropic gas, we study the zero dissipation limit problem of the full 1-D compressible Navier-Stokes equations toward the superposition of contact discontinuity and two rarefaction waves. In the case of both smooth and Riemann initial data, we show that if the solutions to the corresponding Euler system consist of the composite wave of two rarefaction wave and contact discontinuity, then there exist solutions to Navier-Stokes equations which converge to the Riemman solutions away from the initial layer with a decay rate in any fixed time interval as the viscosity and the heat-conductivity coefficients tend to zero. The proof is based on scaling arguments, the construction of the approximate profiles and delicate energy estimates. Notice that we have no need to restrict the strengths of the contact discontinuity and rarefaction waves to be small.

Authors:Mina DINARVAND Pages: 1209 - 1220 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Mina DINARVAND In this paper, we introduce a new geometric constant C N J ( p ) ( a , X ) of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized García-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.

Authors:Turdebek N. Bekjan Pages: 1221 - 1229 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Turdebek N. Bekjan Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let A be a maximal subdiagonal algebra of M. We proved a Szegö type factorization theorem for the Haagerup noncommutative Hp-spaces.

Authors:Dongcheng YANG Pages: 1237 - 1261 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Dongcheng YANG In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method.

Authors:Xiaoni CHI; Hongjin WEI; Zhongping WAN; Zhibin ZHU Pages: 1262 - 1280 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Xiaoni CHI, Hongjin WEI, Zhongping WAN, Zhibin ZHU In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming (CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone (SOC), we reformulate the CCP problem as the second-order cone problem (SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.

Authors:Jianjun HUANG Pages: 1281 - 1294 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Jianjun HUANG Let u = u(t,x, p) satisfy the transport equation ∂ u ∂ t + P p 0 ∂ ∂ x = , where f=f(t, x,p) belongs to Lp ((0,T)× R 3 × R 3) for 1< p <∞ and ∂ ∂ t + P p 0 ∂ ∂ x is the relativistic-free transport operator from the relativistic Boltzmann equation. We show the regularity of ∫ R 3 u ( t , x , p ) d p using the same method as given by Golse, Lions, Perthame and Sentis. This average regularity is considered in terms of fractional Sobolev spaces and it is very useful for the study of the existence of the solution to the Cauchy problem on the relativistic Boltzmann equation.

Authors:Van Hien LE; Dinh Ke TRAN; Trong Kinh CHU Pages: 1295 - 1318 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Van Hien LE, Dinh Ke TRAN, Trong Kinh CHU We study a generalized Cauchy problem associated with a class of impulsive fractional differential inclusions of Sobolev type in Banach spaces. Our aim is to prove the existence of a compact set of globally attracting solutions to the problem in question. An application to fractional partial differential equations subject to impulsive effects is given to illustrate our results.

Authors:Dehua QIU; Pingyan CHEN; Volodin ANDREI Pages: 1319 - 1330 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Dehua QIU, Pingyan CHEN, Volodin ANDREI In this paper, the complete moment convergence for L p -mixingales are studied. Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued Lp -mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.

Authors:Guangzhi DU; Liyun ZUO Pages: 1331 - 1347 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Guangzhi DU, Liyun ZUO In this paper, we consider the mixed Navier-Stokes/Darcy model with Beavers-Joseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.

Authors:Guoqing ZHANG; Weiguo ZHANG; Sanyang LIU Pages: 1348 - 1360 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Guoqing ZHANG, Weiguo ZHANG, Sanyang LIU In this paper, we consider a class of N-Laplacian equations involving critical growth { - Δ N u = λ u N - 2 u + f ( x , u ) , x ∈ Ω , u ∈ W 0 1 , N ( Ω ) , u ( x ) ≥ 0 , x ∈ Ω , where Ω is a bounded domain with smooth boundary in ℝ N (N >2), f (x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ1, λ≠λℓ (ℓ = 2,3,ċċċ), and λℓ is the eigenvalues of the operator ( - Δ N , W 0 1 , N ( Ω ) ) , which is defined by the ℤ2-cohomological index.

Authors:Guangwu WANG; Boling GUO Pages: 1361 - 1372 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Guangwu WANG, Boling GUO In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy. The main techniques is the Faedo-Galerkin approximation and weak compactness theory.

Authors:Rui BU; Jiecheng CHEN; Guoen HU Pages: 1373 - 1384 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Rui BU, Jiecheng CHEN, Guoen HU Let α ∈ ( 0 , n - 1 2 ) and T α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(ℝn) function and T α.

Authors:Biao WANG Pages: 1385 - 1398 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Biao WANG The purpose of this paper is to investigate positive steady states of a diffusive predator-prey system with predator cannibalism under homogeneous Neumann boundary conditions. With the help of implicit function theorem and energy integral method, non-existence of non-constant positive steady states of the system is obtained, whereas coexistence of non-constant positive steady states is derived from topological degree theory. The results indicate that if dispersal rate of the predator or prey is sufficiently large, there is no non-constant positive steady states. However, under some appropriate hypotheses, if the dispersal rate of the predator is larger than some positive constant, for certain ranges of dispersal rates of the prey, there exists at least one non-constant positive steady state.

Authors:Meng YANG Pages: 1399 - 1414 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Meng YANG We give heat kernel estimates on Julia sets J(fc ) for quadratic polynomials fc (z)= z 2 + c for c in the main cardioid or the ± 1 k -bulbs where k ≥2. First we use external ray parametrization to construct a regular, strongly local and conservative Dirichlet form on Julia set. Then we show that this Dirichlet form is a resistance form and the corresponding resistance metric induces the same topology as Euclidean metric. Finally, we give heat kernel estimates under the resistance metric.

Authors:Wei DAI; Zhao LIU Pages: 1415 - 1436 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Wei DAI, Zhao LIU In this paper, we are concerned with the following Hardy-Sobolev type system (0.1) { ( - Δ ) α 2 u ( x ) = υ q ( x ) y t 2 ( - Δ ) α 2 υ ( x ) = u p ( x ) y t 1 , x = ( y , z ) ∈ ( ℝ k \ { 0 } ) × ℝ n - k , where 0<α<n, 0<t 1,t 2 < min{α,k}, and 1 < p ≤ τ 1 : = n + α - 2 t 1 n - α , 1 < q ≤ τ 2 : = n + α - 2 t 2 n - α . . We first establish the equivalence of classical and weak solutions between PDE system (0.2) { u ( x ) = ∫ ℝ n G α ( x , ξ ) u p ( ξ ) η t 2 d ξ υ ( x ) = ∫ ℝ n G α ( x , ξ ) u p ( ξ ) η t 2 d ξ , where G α ( x , ξ ) = c n , α x - ξ n - α is the Green's function of ( - Δ ) α 2 in ℝn. Then, by the method of moving planes in the integral forms, in the critical case p = τ1 and q = τ2, we prove that each pair of nonnegative solutions(u,v) of (0.1) is radially symmetric and monotone decreasing about the origin in ℝk and some point z 0 in ℝn-k. In the subcritical case PubDate: 2017-08-27T16:02:54Z DOI: 10.1016/s0252-9602(17)30082-6

Authors:Yamna BOUKHATEM; Benyattou BENABDERRAHMANE Pages: 1453 - 1471 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Yamna BOUKHATEM, Benyattou BENABDERRAHMANE A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered. Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Authors:Ruyun MA; Hongliang GAO Pages: 1472 - 1482 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Ruyun MA, Hongliang GAO We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian { - ( φ ( u ′ ) ) ′ = λ f ( u ) , x ∈ ( 0 , 1 ) , u ′ ( 0 ) = 0 = u ′ ( 1 ) , where λ is a positive parameter, φ ( s ) = s 1 - s 2 , f ∈ C 1 ( [ 0 , ∞ ) , ℝ ) , f ′ ( u ) > 0 for u > 0 , and for some 0<β<θ such that f(u)<0 for u∈[0,β) (semipositone) and f(u)>0 for u > β. Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C 2([0,β)∪(β,∞),ℝ), f″(u)≥0 for u ∈[0,β) and f″(u) ≤0 for u ∈(β,∞), then there exist exactly 2n+1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.

Authors:Tao HAO; Juan LI Pages: 1497 - 1518 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Tao HAO, Juan LI We establish a new type of backward stochastic differential equations (BSDEs) connected with stochastic differential games (SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs) equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair (W,U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs' condition.

Authors:Zhijuan ZHANG; Xijun YU; Yanzhen CHANG Pages: 1519 - 1535 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Zhijuan ZHANG, Xijun YU, Yanzhen CHANG In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains. The interface may be arbitrary smooth curves. It is shown that the error estimates in L 2-norm for the solution and the flux are O(h 2 logh ) and O(h logh 1/2), respectively. In numerical experiments, the successive substitution iterative methods are used to solve the LDG schemes. Numerical results verify the efficiency and accuracy of the method.

Authors:Feng DU; Chuanxi WU; Guanghan LI; Changyu XIA Pages: 1536 - 1544 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Feng DU, Chuanxi WU, Guanghan LI, Changyu XIA In this paper, we investigate a horizontal Laplacian version of the clamped plate problem on Carnot groups and obtain some universal inequalities. Furthermore, for the lower order eigenvalues of this eigenvalue problem on carnot groups, we also give some universal inequalities.

Authors:Olivier GUIBÉ; Alip OROPEZA Pages: 889 - 910 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Olivier GUIBÉ, Alip OROPEZA In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type { - div ( B ( x , u ) ∇ u ) = f in Ω , u = 0 on Γ o B ( x , u ) ∇ u ⋅ n → + γ ( x ) h ( u ) = g on Γ 1 where f and g are the element of L 1 (Ω) and L 1 (Γ1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique.

Authors:Alberto CABADA; Nikolay D. DIMITROV Pages: 911 - 926 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Alberto CABADA, Nikolay D. DIMITROV This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

Authors:Qun LIU; Daqing JIANG; Ningzhong SHI; Tasawar HAYAT; Ahmed ALSAEDI Pages: 927 - 940 Abstract: Publication date: July 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 4 Author(s): Qun LIU, Daqing JIANG, Ningzhong SHI, Tasawar HAYAT, Ahmed ALSAEDI This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

Authors:Justyna Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Stanisław MIGÓRSKI, Justyna OGORZAŁY We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.

Authors:Feng Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Feng SU The theory of integration to mathematical analysis is so important that many mathematicians continue to develop new theory to enlarge the class of integrable functions and simplify the Lebesgue theory integration. In this paper, by slight modifying the definition of the Henstock integral which was introduced by Jaroslav Kurzweil and Ralph Henstock, we present a new definition of integral on fractal sets. Furthermore, its integrability has been discussed, and the relationship between differentiation and integral is also established. As an example, the integral of Cantor function on Cantor set is calculated.

Authors:Teresa Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Teresa ÁLVAREZ A closed linear relation T in a Banach space X is called left (resp. right) Fredholm if it is upper (resp. lower) semiFredholm and its range (resp. null space) is topologically complemented in X. We say that T is left (resp. right) Browder if it is left (resp. right) Fredholm and has a finite ascent (resp. descent). In this paper, we analyze the stability of the left (resp. right) Fredholm and the left (resp. right) Browder linear relations under commuting Riesz operator perturbations. Recent results of Zivkovic et al. to the case of bounded operators are covered.

Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Ágota P. HORVÁTH We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case. In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials.