Existence and Boundedness of Solutions for Elliptic Equations in General Domains - Elhoussine Azroul; Moussa Khouakhi; Chihab Yazough (Advances in Science, Technology and Engineering Systems Journal, 2017)
This article is devoted to study the existence of solutions for the strongly nonlinear [latex]p(x)[/latex]-elliptic problem: [latex]- Δ_p(x) (u) + α_0 |u|^p(x)-2u = d(x)|u|^p(x)|u|^p(x)+1 + f- div g(x) in Ω, [/latex] [latex]u W_0^1,p(x)(Ω), [/latex] Where [latex]Ω[/latex] is an open set of [latex]R^N[/latex], possibly of infinite measure, we will also give some regularity results for these solutions.
Keywords: Unbounded Domains; Sobolev Spaces With Variable; Exponents; Boundedness Of Solutions; Strongly Nonlinear Elliptic; Equations; Existence Results