渐近线性椭圆方程组的非负解(英文)

Nonnegative Solutions for Asymptotically Linear Elliptic Systems

本文讨论了如下一类渐近线性椭圆方程组{-Δu-μΔv=g(x,v),-Δv-λΔu=f(x,u),x∈Ω,u=v=0,x∈Ω在H01(Ω)×H01(Ω)中至少存在一个非负非平凡的解对(u,v),其中Ω是RN中的一个光滑有界区域,f(x,t)和g(x,t)是Ω×R上的连续函数并且在无穷远处渐近线性.

In this paper,we show that the semilinear elliptic systems of the form{-Δu-μΔv=g(x,v),-Δv-λΔu=f(x,u),x∈Ω,u=v=0,x∈Ωpossess at least one nonnegative nontrivial solution pair(u,v)∈H10(Ω)×H10(Ω),where Ω is a smooth bounded domain in RN,f(x,t)and g(x,t)are continuous functions on Ω×R and asymptotically linear at infinity.