ON A CLASS OF SINGULAR SUPERLINEAR ELLIPTIC SYSTEMS IN A BALL

Abstract

We establish the existence of large positive radial solutions for the elliptic system

\[ łeft\{ begin{c} -Δ u=λ f (v)\enspace text\enspace B , -Δ v=λ g (u)\enspace text\enspace B , u=v=0\enspace text\enspace i B , end i.

\]

when the parameter $\lambda >0$ is small, where $B$ is the open unit ball $ \mathbb{R}^{N},N>2, f,g:(0,\infty )\rightarrow \mathbb{R}$ are possibly singular at 0 and $f (u)\sim u^{p},g (v)\sim v^{q}$ at $\infty $ for some $ p,q>0$ with $pq>1.\ $Our approach is based on fixed point theory in a cone.