Multiple solutions for a elliptic system in exterior domain

Abstract

In this paper, we study the existence of solutions for the nonlinear elliptic system $$displaylines{ -Delta u+u=|u|^{p-1}u+lambda v quad hbox{in } Omega, cr -Delta v+v=|v|^{p-1}v+lambda u quad hbox{in } Omega, cr u=v=0 quad hbox{on } partialOmega, }$$ where $Omega$ is a exterior domain in $mathbb{R}^N$, $Ngeq 3$. We show that the system possesses at least one nontrivial positive solution.

Keywords

• Exterior domain
• nonlinear elliptic system
• existence result