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

Abstract

In this paper we prove a strong comparison principle for radially decreasing solutions u, v ∈ C 1,α 0 ( BR ) of the singular equationsHere we assume that 1 < p < 2, δ ∈ (0, 1) and f, g are continuous, radial functions such that 0 ≤ f ≤ g but f ≡ g in B R . For the case p > 2 a counterexample is provided where the strong comparison principle is violated. As an application of strong comparison principle, we prove a three solution theorem for p-Laplace equation and illustrate with an example.