A note on multiple solutions for sublinear elliptic systems

Abstract

We prove the existence of a sequence of solutions approaching zero for an elliptic system of the form $-\Delta u=|v|^{q-2}v+g(x,v)$, $-\Delta v=|u|^{p-2}u+f(x,u)$ in a bounded domain, under Dirichlet homogeneous boundary conditions. We assume that $1 <p,q <2$ and that both $f(x,u)$ and $g(x,v)$ are small enough near the origin.