Existence of solutions for sublinear equations on exterior domains

Abstract

In this article we consider the radial solutions of $\Delta u + K(r)f(u)= 0$ on the exterior of the ball of radius $R>0$, $B_{R}$, centered at the origin in ${\mathbb R}^N$ with $u=0$ on $\partial B_{R}$ and $\lim_{r \to \infty} u(r)=0$ where $N>2$, $f$ is odd with $f0$ on $(\beta, \infty)$, $f(u)\sim u^p$ with $00$ is sufficiently small. If $R>0$ is sufficiently large then there are no solutions with $\lim_{r \to \infty} u(r)=0$.

Keywords

• Exterior domains
• semilinear
• sublinear
• radial solution