Positive solutions for a class of quasilinear singular equations

Abstract

This article concerns the existence and uniqueness of solutions to the quasilinear equation -Δpu = ρ(x)ƒ(u) in ℝN with u > 0 and u(x) → 0 as |x| → ∞. Here 1 < p < ∞, N ≥ 3, Δp is the p-Laplacian operator, ρ and ƒ are positive functions, and ƒ is singular at 0. Our approach uses fixed point arguments, the shooting method, and a lower-upper solutions argument.