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

2022/03/22 by R. Dhanya, Dhanya, R., M. S. Indulekha +3
Engineering · Mathematics · #35J66 #35J75 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.11477

openalex publication_date 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a strong comparison principle for radially decreasing solutions u,v∈ C₀^1,α(\BarB_R) of the singular equations -Δ_p u-(1)/(u^δ)=f(x) and -Δ_p v-(1)/(v^δ)=g(x) in B_R. Here we assume that 12 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.

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