Existence and nonexistence of nontrivial weak solution for a class of general capillarity systems

The aim of this paper is to study the nonexistence and existence of nonnegative, nontrivial weak solution for a class of general capillarity systems. The proofs rely essentially on the minimum principle combined with the mountain pass theorem.     

PERIODIC AND ALMOST PERIODIC SOLUTIONS OF A CERTAIN INFINITE DELAY INTEGRAL EQUATION

In this paper,by using successive approximation method and fixed-point theorem,we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the peri- odic and almost periodic solutions of the system.     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS OF DELAYED BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS

In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring the existence, uniqueness and global stability of periodic solution. These results are helpful to design global exponential stable BAM networks and periodic oscillatory BAM networks.     

DECOMPOSITION, REPRESENTATION AND EXTENSION OF THE HARMONIC FUNCTIONS

In this paper, by using the probabilistic method, we obtained a decomposition theorem for the harmonic functions, generalized and strengthened some theorems: Doob's theorem on the limit behaviors of the superharmonic functions, Bocher's theorem on the representation of the harmonic functions and the extension theorem of the harmonic functions etc.     

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values.This paper provides a natural condition of the existence of stable pcsitive steady-state solutions for the one predator two prey system.Under this conditon we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem,discuss the positive stable solution problem bifureated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.     

A GENERAL FORM OF THE INCREMENTS OF A TWO-PARAMETER WIENER PROCESS

In this paper,we consider a general form of the increments for a two-parameter Wiener process.Both the Csorgo-Revesz‘s increments and a class of the lag increments are the special cases of this general form of increments.Our results imply the theorem that have been given by Csorgo and Revesz(1978),and some of their conditions are removed.     

THE EXISTENCE OF ALMOST PERIODIC SOLUTION TO A CLASS OF ALMOST PERIODIC DIFFERENTIAL SYSTEM

By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of n-dimensional almost periodic systems, which is more general than the systems in [1-2]. We generalize and improve some results in [3].     

EXISTENCE OF NON-OSCILLATORY SOLUTIONS OF A CLASS OF HIGHER-ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH A FORCED TERM

In this paper, we consider a certain forced higher-order nonlinear neutral difference equation. By using Krasnoselskii's fixed point theorem and some new techniques, we obtain necessary and sufficient conditions for the existence of non-oscillatory solutions for the system. Our results extend the results of Zhang [5].     

Multiple Solutions for a Differential Inclusion Problem with Nonhomogeneous Boundary Conditions

In this paper, we use a mountain pass theorem with Cerami type conditions for locally Lipschitz functions to investigate the existence of at least one nontrivial solution for a differential inclusion problem involving the p-Laplacian and with nonlinear and nonsmooth boundary conditions. Moreover, by a symmetric version of the mountain pass theorem, we prove the existence of infinitely many solutions.     

On a quasilinear Schrödinger-Poisson system

In this paper we study a quasilinear elliptic system coupled by a Schrödinger equation with p-Laplacian operator and a Poisson equation. Some scaling transformation and ingenious methods are applied to produce the bounded Palais-Smale sequences and the existence of nontrivial solutions for the system is obtained by the mountain pass theorem.     

Periodic solutions for a nonlinear (q,p)-Laplacian dynamical system with impulsive effects

In this paper, some existence theorems are obtained for periodic solutions of a nonlinear (q,p)-Laplacian dynamical system with impulsive effects by using the least action principle and mountain pass theorem.     

Multiplicity of solutions for a quasilinear elliptic problem via the cohomological index

In this paper we study a quasilinear elliptic problem with the Dirichlet boundary condition in a bounded domain involving the operator Au=−Δ_pu−Δ_qu. Assuming that the nonlinearity has a concave-convex behavior we obtain some multiplicity results. More precisely, we obtain five nontrivial solutions; two by a minimization argument, two by the mountain pass theorem, and the other by a cohomological linking theorem.     

一类椭圆型半变分不等式解的存在性(英文)

本文研究了一类Dirichlet边界的椭圆型半变分不等式问题.利用非光滑形式的环绕定理和非光滑形式的对称山路定理,得到了在相应假设条件下此不等式问题至少有一个非平凡解和无穷多解.本文中非光滑势能在原点处关于算子+V(x)的第一正特征值λ是不完全共振的.     

Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities

We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l>2 and (IIl), l?1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.     

Mountain pass theorems without Palais–Smale conditions

Using nonstandard analysis, we will prove two new mountain pass theorems which cannot be obtained from the well known classical mountain pass theorem of Ambrosetti–Rabinowitz.     

Schrödinger-Poisson equations without Ambrosetti-Rabinowitz condition

We prove the existence of ground state solutions for a stationary Schrödinger-Poisson equation in R³. The proof is based on the mountain pass theorem and it does not require the Ambrosetti-Rabinowitz condition.     

Soliton solutions for quasilinear Schrödinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].     

一类渐近线性双调和方程非平凡解的存在性

通过建立新空间H,证明了一个嵌入定理.进一步,利用该嵌入定理与山路引理得到了一类渐近线性双调和问题在空间H中非平凡解的存在性.