Strong comparison principle for a p-Laplace equation involving singularity and its applications

Abstract

We prove a strong comparison principle for radially decreasing solutions u,v∈C01,α(BR¯) of the singular equations −Δpu−λuδ=f(x) and −Δpv−λvδ=g(x) in BR, where 1<p≤2,δ∈(0,1) and λ>0. We assume that f and g are continuous radial functions with 0≤f≤g and f⁄≡g in BR. Also, a counterexample is provided where the strong comparison principle is violated when p>2. In addition, we prove a three solution theorem for p-Laplace equation as an application of strong comparison principle. This is illustrated with an example.