Effect of Non-linear Lower Order Terms in Quasilinear Equations Involving the p(x)-Laplacian

2020/04/29 by Pablo Ochoa, Analia Silva, Ochoa, Pablo +1
Mathematics · #35A01 #35D30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A01 #msc:35D30

paper · pdf · doi:10.48550/arxiv.2004.14300

21 pages, no figures

arxiv created 2020/04/29 · arxiv updated 2020/04/30

Abstract

In this work, we study the existence of W₀^{1, p(⋅)}-solutions to the following boundary value problem involving the p(⋅)-Laplacian operator: \lbrace -Δ_p(x)u+|∇ u|^q(x)=λg(x)u^η(x)+f(x), \textnormal in Ω,
u≥ 0, \textnormal in Ω u= 0, on ∂Ω. .under appropriate ranges on the variable exponents. We give assumptions on f and g in terms of the growth exponents q and η under which the above problem has a non-negative solution for all λ> 0.

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