Positive Radial Solutions for Singular Quasilinear Elliptic Equations in a Ball

Abstract

We establish the existence of positive radial solutions for the boundary value problems

where ${\Delta }_{p}u=\text{div}(|\nabla u{|}^{p-2}\nabla u),p\ge 2$, $B$ is the open unit ball ${\mathbb{R}}^N$, $\lambda$ is a positive parameter, and $f:(0,\infty )\to \mathbb{R}$ is $p$-superlinear at $\infty$ and is allowed to be singular at $0$.