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 {\...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-08-01
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| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/msds-2020-0133 |
| _version_ | 1818322747023949824 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-13T11:01:42Z |
| format | Article |
| id | doaj.art-76816fc6f9d54ec9947112a92b13f407 |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-12-13T11:01:42Z |
| publishDate | 2021-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-76816fc6f9d54ec9947112a92b13f4072022-12-21T23:49:13ZengDe GruyterNonautonomous Dynamical Systems2353-06262021-08-018118020610.1515/msds-2020-0133Existence of renormalized solutions for some quasilinear elliptic Neumann problemsBenboubker Mohamed Badr0Hjiaj Hassane1Ibrango Idrissa2Ouaro Stanislas3Ecole Nationale des Sciences Appliquées (ENSA), Université Abdelmalek Essaadi, B.P 2222 M’hannech Tétouan, MarocDépartement de Mathématiques, Faculté des Sciences de Tétouan, Université Abdelmalek Essaadi, B.P. 2121, Tétouan, MarocLAboratoire de Mathématiques et Informatique (LAMI), UFR. Sciences et Techniques, Université Polytechnique de Bobo-Dioulasso, 01 BP 1091 Bobo 01, Bobo-Dioulasso, Burkina FasoLAboratoire de Mathématiques et Informatique (LAMI), UFR. Sciences Exactes et Appliquées, Université de Ouagadougou, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina FasoThis 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.https://doi.org/10.1515/msds-2020-0133renormalized solutionstrongly nonlinear elliptic equationsanisotropic variable exponent sobolev spacesneumann problem35j6035d05 |
| spellingShingle | Benboubker Mohamed Badr Hjiaj Hassane Ibrango Idrissa Ouaro Stanislas Existence of renormalized solutions for some quasilinear elliptic Neumann problems Nonautonomous Dynamical Systems renormalized solution strongly nonlinear elliptic equations anisotropic variable exponent sobolev spaces neumann problem 35j60 35d05 |
| title | 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_short | Existence of renormalized solutions for some quasilinear elliptic Neumann problems |
| title_sort | existence of renormalized solutions for some quasilinear elliptic neumann problems |
| topic | renormalized solution strongly nonlinear elliptic equations anisotropic variable exponent sobolev spaces neumann problem 35j60 35d05 |
| url | https://doi.org/10.1515/msds-2020-0133 |
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