具奇异源p-Laplace方程的多重径向正解

考虑具非齐次边值条件的p-Laplace方程多重径向正解的存在性,借助于Guo-Krasnoselskii锥不动点定理,得到了至少三个径向正解的存在性.     

全空间上一类半线性双调和方程正解的衰减

研究如下非齐次双调和方程-△~2u+u~p+f(x)=0,x∈R~n(*)正解的存在性,其中△~2是双调和算子,p1,n≥5,f≠0.在文献[16[的基础上,得到:对f给定条件,方程(*)有一类不同于文献[16]的两种衰减的正解.     

一个捕食椭圆型方程组正解的存在性、唯一性与稳定性

研究一个修正的Leslie-Gower和 Holling-Type II型的捕食模型的椭圆型方程组的齐次Dirichlet边值问题的正解. 给出了存在性、 唯一性、不存在性、分支和稳定性. 特别地, 得到了连接半平凡解和极限方程的唯一正解的连通分支.     

一类带有交叉扩散的捕食-食饵模型的正解

该文研究了一类在齐次Dirichlet边界条件下的带有交叉扩散的捕食-食饵模型.首先,根据Leray-Schauder度理论,建立了系统的正解的存在性;其次,当参数m=且充分大时,分别研究了正则扰动方程和奇异扰动方程的正解的存在性,和借助分歧理论说明奇异系统的正解在a~*处爆破;最后,建立了系统正解的多解性.     

一类带有交错扩散的捕食模型非常数正解的进一步分析

本文讨论一个带有交错扩散的捕食模型的齐次Neumann问题.首先,利用Harnack等式以及椭圆方程正则理论讨论了当扩散系数至少一个取极限时非常数正解的渐近性,再利用渐近性质以及奇异扰动方法讨论了当扩散系数取极限的情况下非常数正解的存在性.     

退化变分问题和退化椭圆型方程的正解

本文讨论由未知函数u=0引起的下列退化变分问题正解的存在性: 证明此正解满足Harnack不等式性质,进一步讨论带自然增长退化椭圆型Euler方程具下列非齐次Dirichlet问题解的存在性:     

具Hardy-Sobolev界指数的非齐次椭圆方程的正解

讨论-类具Hardy-Sobolev临界指数的非齐次半线性椭圆方程,通过应用Lions集中紧性原理建立了S_μ(Q)的极小函数,再结合Ekeland变分原理、山路引理和Nehari流形的分析方法证明了方程在适当条件下正解的存在性与多重性.     

退化变分问题和退化椭圆型方程的正解

本文讨论由未知函数 u=0引起的下列退化变分问题正解的存在性:证明此正解满足 Harnack 不等式性质,进一步讨论带自然增长退化椭圆型 Euler 方程具下列非齐次 Dirichlet 问题解的存在性:     

关于含非齐次Dirichlet边值的Brzis-Nirenberg问题的研究

该文研究了含非齐次Dirichlet边值的Brezis-Nirenberg方程对应泛函的Nehari流形的结构.并结合Lusternik-Schnirelman畴数理论和极大极小原理,证明了含非齐次Dirichlet边值的Brezis-Nirenberg方程存在4个正解.     

拟线性椭圆方程的衰减正解

本文建立了一类拟线性椭圆方程具有高度衰减阶正解的存在性，并对此类正解的最大值进行了上下界估计。     

On strong solutions to the compressible Hall-magnetohydrodynamic system

In this paper, we consider strong/classical solutions to the 3D compressible Hall-magnetohydrodynamic system. First, we prove the existence of local strong solutions with positive density. Then the existence of global small solutions with small initial data is proved. Optimal time decay rate is also established.     

Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity

In this paper, we are concerned with the existence of positive solutions for a class of fractional Schrödinger–Poisson system with critical nonlinearity and multiple competing potentials, which may decay and vanish at infinity. Under some local conditions, we show the existence and concentration of positive solutions by using the modified penalization method and concentration–compactness principle.     

Stability of solution for a mixture of thermoelastic of type III

In this work, we analyze the existence, uniqueness, and asymptotic behavior of solution to the model of a thermoelastic mixture of type III. We establish sufficient conditions to guarantee the exponential decay of solutions. When the decay is not of exponential type, we prove that the solutions decay polynomially and we find the optimal polynomial decay rate. Copyright © 2017 John Wiley & Sons, Ltd.     

Multibump solutions for discrete periodic nonlinear Schrödinger equations

In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity.     

Stability of a von Karman equation with infinite memory

In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history.     

Global existence,asymptotic stability and blow-up of solutions for the generalized Boussinesq equation with nonlinear boundary condition

In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish firstly the local existence of solutions by standard Galerkin method. Then we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow-up result for solutions with positive and negative initial energy respectively.     

Existence and general decay for nondissipative distributed systems with boundary frictional and memory dampings and acoustic boundary conditions

In this paper, we study the existence and general energy decay rate of global solutions for nondissipative distributed systems

$$u''-\triangle u+h(\nabla u)=0$$

with boundary frictional and memory dampings and acoustic boundary conditions. For the existence of solutions, we prove the global existence of weak solution by using Faedo–Galerkin’s method and compactness arguments. For the energy decay rate, we first consider the general nonlinear case of h satisfying a smallness condition and prove the general energy decay rate by using perturbed modified energy method. Then, we consider the linear case of h: \({h(\nabla u)=-\nabla\phi\cdot\nabla u}\) and prove the general decay estimates of equivalent energy.

     

Optimal decay rates and the selfadjoint property in overdamped systems

We deal with abstract linear strongly damped wave equations. In the so-called overdamped regime we show the occurrence of two interesting phenomena. The first is the existence of an explicit special inner product which makes the problem selfadjoint. The second is an improvement of the decay rate for more regular solutions that will be of an exponential-polynomial type. Furthermore, we prove the optimality of this decay rate.     

Positive Solutions for a Lotka–Volterra Prey–Predator Model with Cross-Diffusion of Fractional Type

In this paper we consider a Lotka–Volterra prey–predator model with cross-diffusion of fractional type. The main purpose is to discuss the existence and nonexistence of positive steady state solutions of such a model. Here a positive solution corresponds to a coexistence state of the model. Firstly we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system. Secondly we derive some necessary conditions to ensure the existence of positive solutions, which demonstrate that if the intrinsic growth rate of the prey is too small or the death rate (or the birth rate) of the predator is too large, the model does not possess positive solutions. Thirdly we study the sufficient conditions to ensure the existence of positive solutions by using degree theory. Finally we characterize the stable/unstable regions of semi-trivial solutions and coexistence regions in parameter plane.