Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces

In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. By using a lin...

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Autores principales:	Ge Dong, Xiaochun Fang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1e8d288e5550485b8913742e5f0d0855
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spelling	oai:doaj.org-article:1e8d288e5550485b8913742e5f0d08552021-11-29T00:57:10ZBarrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces2314-888810.1155/2021/9927898https://doaj.org/article/1e8d288e5550485b8913742e5f0d08552021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/9927898https://doaj.org/toc/2314-8888In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. By using a linear functional analysis method, we provide sufficient conditions which ensure that the solution set of the equation is nonempty, and it possesses a greatest element and a smallest element with respect to the ordering “≤,” which are called barrier solutions.Ge DongXiaochun FangHindawi LimitedarticleMathematicsQA1-939ENJournal of Function Spaces, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Ge Dong Xiaochun Fang Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
description	In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. By using a linear functional analysis method, we provide sufficient conditions which ensure that the solution set of the equation is nonempty, and it possesses a greatest element and a smallest element with respect to the ordering “≤,” which are called barrier solutions.
format	article
author	Ge Dong Xiaochun Fang
author_facet	Ge Dong Xiaochun Fang
author_sort	Ge Dong
title	Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
title_short	Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
title_full	Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
title_fullStr	Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
title_full_unstemmed	Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces
title_sort	barrier solutions of elliptic differential equations in musielak-orlicz-sobolev spaces
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/1e8d288e5550485b8913742e5f0d0855
work_keys_str_mv	AT gedong barriersolutionsofellipticdifferentialequationsinmusielakorliczsobolevspaces AT xiaochunfang barriersolutionsofellipticdifferentialequationsinmusielakorliczsobolevspaces
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Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces

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