一类二阶半线性椭圆方程多重解的存在性

On the Existence of Multiple Solutions for Some Second Order Semilinear Elliptic Equation

利用变型环绕理论,研究了当λk<λ<λk+1时二阶半线性椭圆方程-Δu=λa(x)u+p(x,u)在Ω内的非平凡解的存在性。其中,Ω是RN上的有界开集;Ω是平滑边界。

By using a variation of linking theorem,under condition of λk〈λ〈λk＋1,the paper investigates the existence of nontrivial solutions of a second order semilinear elliptic boundary value problem with Dirichlet boundary condition,-Δu=λa（x）u＋p（x,u） in Ω,where Ω is a bounded open set in RN with smooth boundary Ω.