Existence of renormalized solutions for some quasilinear elliptic Neumann problems

This paper is devoted to study some nonlinear elliptic Neumann equations of the type{Au+g(x,u,∇u)+|u|q(⋅)-2u=f(x,u,∇u)inΩ,∑i=1Nai(x,u,∇u)⋅ni=0on∂Ω,\left\{ {\matrix{ {Au + g(x,u,\nabla u) + |u{|^{q( \cdot ) - 2}}u = f(x,u,\nabla u)} \hfill & {{\rm{in}}} \hfill & {\Omega ,} \hfill \cr {\...

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Autores principales:	Benboubker Mohamed Badr, Hjiaj Hassane, Ibrango Idrissa, Ouaro Stanislas
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	renormalized solution strongly nonlinear elliptic equations anisotropic variable exponent sobolev spaces neumann problem 35j60 35d05 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/76816fc6f9d54ec9947112a92b13f407
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spelling	oai:doaj.org-article:76816fc6f9d54ec9947112a92b13f4072021-12-05T14:10:56ZExistence of renormalized solutions for some quasilinear elliptic Neumann problems2353-062610.1515/msds-2020-0133https://doaj.org/article/76816fc6f9d54ec9947112a92b13f4072021-08-01T00:00:00Zhttps://doi.org/10.1515/msds-2020-0133https://doaj.org/toc/2353-0626This paper is devoted to study some nonlinear elliptic Neumann equations of the type{Au+g(x,u,∇u)+\|u\|q(⋅)-2u=f(x,u,∇u)inΩ,∑i=1Nai(x,u,∇u)⋅ni=0on∂Ω,\left\{ {\matrix{ {Au + g(x,u,\nabla u) + \|u{\|^{q( \cdot ) - 2}}u = f(x,u,\nabla u)} \hfill & {{\rm{in}}} \hfill & {\Omega ,} \hfill \cr {\sum\limits_{i = 1}^N {{a_i}(x,u,\nabla u) \cdot {n_i} = 0} } \hfill & {{\rm{on}}} \hfill & {\partial \Omega ,} \hfill \cr } } \right. in the anisotropic variable exponent Sobolev spaces, where A is a Leray-Lions operator and g(x, u, ∇u), f (x, u, ∇u) are two Carathéodory functions that verify some growth conditions. We prove the existence of renormalized solutions for our strongly nonlinear elliptic Neumann problem.Benboubker Mohamed BadrHjiaj HassaneIbrango IdrissaOuaro StanislasDe Gruyterarticlerenormalized solutionstrongly nonlinear elliptic equationsanisotropic variable exponent sobolev spacesneumann problem35j6035d05MathematicsQA1-939ENNonautonomous Dynamical Systems, Vol 8, Iss 1, Pp 180-206 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	renormalized solution strongly nonlinear elliptic equations anisotropic variable exponent sobolev spaces neumann problem 35j60 35d05 Mathematics QA1-939
spellingShingle	renormalized solution strongly nonlinear elliptic equations anisotropic variable exponent sobolev spaces neumann problem 35j60 35d05 Mathematics QA1-939 Benboubker Mohamed Badr Hjiaj Hassane Ibrango Idrissa Ouaro Stanislas Existence of renormalized solutions for some quasilinear elliptic Neumann problems
description	This paper is devoted to study some nonlinear elliptic Neumann equations of the type{Au+g(x,u,∇u)+\|u\|q(⋅)-2u=f(x,u,∇u)inΩ,∑i=1Nai(x,u,∇u)⋅ni=0on∂Ω,\left\{ {\matrix{ {Au + g(x,u,\nabla u) + \|u{\|^{q( \cdot ) - 2}}u = f(x,u,\nabla u)} \hfill & {{\rm{in}}} \hfill & {\Omega ,} \hfill \cr {\sum\limits_{i = 1}^N {{a_i}(x,u,\nabla u) \cdot {n_i} = 0} } \hfill & {{\rm{on}}} \hfill & {\partial \Omega ,} \hfill \cr } } \right. in the anisotropic variable exponent Sobolev spaces, where A is a Leray-Lions operator and g(x, u, ∇u), f (x, u, ∇u) are two Carathéodory functions that verify some growth conditions. We prove the existence of renormalized solutions for our strongly nonlinear elliptic Neumann problem.
format	article
author	Benboubker Mohamed Badr Hjiaj Hassane Ibrango Idrissa Ouaro Stanislas
author_facet	Benboubker Mohamed Badr Hjiaj Hassane Ibrango Idrissa Ouaro Stanislas
author_sort	Benboubker Mohamed Badr
title	Existence of renormalized solutions for some quasilinear elliptic Neumann problems
title_short	Existence of renormalized solutions for some quasilinear elliptic Neumann problems
title_full	Existence of renormalized solutions for some quasilinear elliptic Neumann problems
title_fullStr	Existence of renormalized solutions for some quasilinear elliptic Neumann problems
title_full_unstemmed	Existence of renormalized solutions for some quasilinear elliptic Neumann problems
title_sort	existence of renormalized solutions for some quasilinear elliptic neumann problems
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/76816fc6f9d54ec9947112a92b13f407
work_keys_str_mv	AT benboubkermohamedbadr existenceofrenormalizedsolutionsforsomequasilinearellipticneumannproblems AT hjiajhassane existenceofrenormalizedsolutionsforsomequasilinearellipticneumannproblems AT ibrangoidrissa existenceofrenormalizedsolutionsforsomequasilinearellipticneumannproblems AT ouarostanislas existenceofrenormalizedsolutionsforsomequasilinearellipticneumannproblems
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Existence of renormalized solutions for some quasilinear elliptic Neumann problems

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