具有Fucik谱共振的Kirchhoff方程非平凡解的存在性

主要通过变分法得到一类在无穷远处具有Fucik谱共振的Kirchhoff型方程{-(∫Ω|▽u|^(2)dx)Δu=α(u+)^(3)+β(u-)^(3)+f(x,u)x∈Ωu=0x∈∂Ω非平凡解的存在性.其中Ω是RN(N=1,2,3)中的开球,α,β∈R,u+=max{u,0},u-=min{u,0},u=u++u-.非线性项f∈C(Ω×R,R)满足f(x,0)=0.应用带有(Ce)条件的山路定理,得到该方程在Fucik谱的两条平凡曲线上非平凡解的存在性.

Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity

In this paper,Fucik spectrum,ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and some new results on the existence of nontrivial solutions,multiple solutions and sign-changing solutions are obtained.In one case seven nontrivial solutions are got.The techniques have independent interest.

一类带权函数的拟线性椭圆方程

该文利用变分方法讨论了方程-△pu=λa(x)(u+)p-1-μa(x)(u-)p-1+f(x,u),u∈W01,p(Ω)在(λ,μ)■∑p和(λ,μ)∈∑p两种情况下的可解性,其中Ω是RN(N≥3)中的有界光滑区域,∑p为方程-△pu=αa(x)(u+)p-1-βa(x)(u-)p-1,u∈W01,p(Ω)的Fucik谱,权重函数a(x)∈Lτ(Ω)(r≥N／p)且a(x)>0 a．e．于Ω,f满足一定的条件．

具有不对称非线性项二阶微分方程的周期解

研究了一类具有非线性项二阶Duffing方程解的一些性质 。

一类p-Laplacian的广义的Fuik谱

We consider the FuAcˇik spectrum of p-Laplacian equation -Δpu=αa（x）（u+）p-1+(βa（x）（u-）p-1 x)∈Ω,u=0,x∈Ω in Ω,u=0 on Ω,where Ω is a bounded smooth domain in RN（N≥1） with boundray Ω.We apply a variant of mountain-pass above equation.Furthermore,we also get a nontrivial solution of a nonresonance problem.

跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.

带跳跃非线性项的p-Laplacian问题的结点解

研究了带跳跃非线性项的p-Laplacian方程结点解的存在性.如果该问题的非线性项跨越其对应齐次问题的Fucik谱,我们证明了该问题至少存在一个结点解.

Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems

In the present paper, the author studies the existence of sign-changing solutions for nonlinear elliptic equations, which have jumping nonlinearities, and may or may not be resonant with respect to Fucik spectrum, via linking methods under Cerami condition.