New existence of periodic solutions for second order non-autonomous Hamiltonian systems

By using mountain pass theorem and local link theorem, some existence theorems are obtained for periodic solutions of second order non-autonomous Hamiltonian systems under local superquadratic condition and other suitable conditions.     

Multiple Positive Solutions for a Nonlinear Elliptic Equation Involving Hardy–Sobolev–Maz'ya Term

In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy–Sobolev–Maz'ya term:-Δu- λu/|y|2=|u|pt-1u/|y|t+ μf(x), x ∈Ω,where Ω is a bounded domain in RN(N ≥ 2), 0 ∈Ω, x =(y, z) ∈ Rk× RN-kand pt =N +2-2t N-2(0 ≤ t ≤2). For f(x) ∈ C1(Ω)\{0}, we show that there exists a constant μ* 0 such that the problem possessesat least two positive solutions if μ∈(0, μ*) and at least one positive solution if μ = μ*. Furthermore,there are no positive solutions if μ∈(μ*, +∞).     

Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type , where δ>0 is the ratio of odd positive integers, {p_n} and {q_n} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.     

Homoclinic solutions for a class of nonperiodic and noneven second-order Hamiltonian systems

The existence of homoclinic solutions is obtained for second-order Hamiltonian systems , as the limit of the solutions of a sequence of nil-boundary-value problems which are obtained by the Mountain Pass theorem, when L(t) and W(t,x) are neither periodic nor even with respect to t.     

A unified proof on existence of homoclinic orbits for some semilinear ordinary differential equations with periodic potentials

This paper gives a direct, short and unified proof of Rabinowitz's Theorem, Grossinho-Minhós-Tersian's Theorem and Tersian-Chaparova's Theorems on existence of homoclinic orbits for second order periodic Hamiltonian systems, fourth and sixth order periodic ordinary differential equations, respectively, by Brezis-Nirenberg type Mountain Pass Lemma.     

Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities

In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation $$ \left\{ - \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3, \right. $$ where $1相似文献   

Nonuniformly nonlinear elliptic equations of p-biharmonic type

This paper deals with the existence and multiplicity of weak solutions to nonlinear differential equations involving a general p-biharmonic operator (in particular, p-biharmonic operator) under Dirichlet boundary conditions or Navier boundary conditions. Our method is mainly based on variational arguments.     

一类P—Laplace方程正解的存在性

本文在不满足(AR)条件下,利用山路引理,证明了P-Laplace方程Dirichlet问题正解的存在性.