Existence and multiplicity of solutions to a p-q Laplacian system with a concave and singular nonlinearities

2020/05/11 by Debajyoti Choudhuri, Choudhuri, Debajyoti, Kamel Saoudi +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2005.05167

openalex publication_date 2020/05/11 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence of multiple nontrivial positive weak solutions to the following system of problems. \beginsplit -Δ_pu-Δ_q u amp;= λf(x)|u|^r-2u+ν(1-α)/(2-α-β)h(x) |u|^-α|v|^1-β in Ω,
-Δ_pv-Δ_q v amp;= μg(x)|v|^r-2v+ν(1-β)/(2-α-β)h(x) |u|^1-α|v|^-β in Ω,
u,vamp;gt;0 in Ω,
u= v amp;= 0 on ∂Ω\endsplit where (C):~0

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