Positive solutions for a class of quasilinear singular equations

Abstract

This article concerns the existence and uniqueness of solutions to the quasilinear equation $$ -Delta_p u= ho(x) f(u) quad hbox{in } mathbb{R}^N $$ with $u > 0$ and $u(x)o 0$ as $|x| o infty$. Here $1 < p < infty$, $N geq 3$, $Delta_{p}$ is the $p$-Laplacian operator, $ ho$ and $f$ are positive functions, and $f$ is singular at 0. Our approach uses fixed point arguments, the shooting method, and a lower-upper solutions argument.

Keywords

• Singular equations
• radial positive solutions
• fixed points
• shooting method
• lower-upper solutions.