Nonnegative Solutions for Asymptotically Linear Elliptic Systems
Jianfu Yang · Mathematica Applicata · 2009
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.