一类渐近线性方程非平凡解的存在性

Existence of Nontrivial Solutions for a Class of Asymptotically Linear Equation

利用山路定理,研究了一类半线性椭圆方程-△u=f(x,u),x∈Ω在H_0~1(Ω)中至少存在一个非平凡解,其中Ω为R^N中的光滑有界区域,N≥3,f(x,t)为Ω×R上的连续函数并且当t→∞时关于t渐近线性.

By using the mountain pass theorem, we show that the semilinear elliptic equation-Δu=f（x,u）,x∈Ωpossesses at least one nontrivial solution in H0^1（Ω）, whereΩis a bounded smooth domain in R^N, N≥3, f（x,t） isa continuous function onΩ×R and asymptotically linear as t→∞.