Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data
In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type {Au+g(x,u,∇u)=μ−div φ(u)in Ω,u=0on ∂Ω,\left\{ {\matrix{{Au + g\left( {x,u,\nabla u} \right) = \mu - div\,\phi \left( u \right)} \hfill & {in\,\Omega ,} \hfill \cr {u = 0} \hfil...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-06-01
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| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/msds-2022-0147 |
| _version_ | 1827998209723596800 |
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| author | Al-Hawmi Mohammed Hjiaj Hassane |
| author_facet | Al-Hawmi Mohammed Hjiaj Hassane |
| author_sort | Al-Hawmi Mohammed |
| collection | DOAJ |
| description | In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type
{Au+g(x,u,∇u)=μ−div φ(u)in Ω,u=0on ∂Ω,\left\{ {\matrix{{Au + g\left( {x,u,\nabla u} \right) = \mu - div\,\phi \left( u \right)} \hfill & {in\,\Omega ,} \hfill \cr {u = 0} \hfill & {on\,\,\partial \Omega ,} \hfill \cr } } \right.
where Au=−∑i=1N∂∂xiai(x,u,∇u)Au = - \sum\limits_{i = 1}^N {{\partial \over {\partial {x_i}}}{a_i}\left( {x,u,\nabla u} \right)} is a Leray-Lions operator, the Carathéodory function g(x, s, ξ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data µ = f − div F belongs to L1−dual and ϕ (·) ∈ C0(R, RN). |
| first_indexed | 2024-04-10T05:41:14Z |
| format | Article |
| id | doaj.art-9e2f65d3994b40f8b82e6dd658dfe993 |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-04-10T05:41:14Z |
| publishDate | 2022-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-9e2f65d3994b40f8b82e6dd658dfe9932023-03-06T10:26:16ZengDe GruyterNonautonomous Dynamical Systems2353-06262022-06-0191689010.1515/msds-2022-0147Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure dataAl-Hawmi Mohammed0Hjiaj Hassane1Department of Mathematics, Faculty of Education and Sciences, University of Saba Region, Marib, YemenDepartment of Mathematics, Faculty of Sciences, University Abdelmalek Essaadi, BP 2121, Tetouan, MoroccoIn this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type {Au+g(x,u,∇u)=μ−div φ(u)in Ω,u=0on ∂Ω,\left\{ {\matrix{{Au + g\left( {x,u,\nabla u} \right) = \mu - div\,\phi \left( u \right)} \hfill & {in\,\Omega ,} \hfill \cr {u = 0} \hfill & {on\,\,\partial \Omega ,} \hfill \cr } } \right. where Au=−∑i=1N∂∂xiai(x,u,∇u)Au = - \sum\limits_{i = 1}^N {{\partial \over {\partial {x_i}}}{a_i}\left( {x,u,\nabla u} \right)} is a Leray-Lions operator, the Carathéodory function g(x, s, ξ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data µ = f − div F belongs to L1−dual and ϕ (·) ∈ C0(R, RN).https://doi.org/10.1515/msds-2022-0147unilateral problemnonlinear elliptic equationsanisotropic sobolev spacesentropy solutionsmeasure data35j1535j62 |
| spellingShingle | Al-Hawmi Mohammed Hjiaj Hassane Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data Nonautonomous Dynamical Systems unilateral problem nonlinear elliptic equations anisotropic sobolev spaces entropy solutions measure data 35j15 35j62 |
| title | Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data |
| title_full | Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data |
| title_fullStr | Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data |
| title_full_unstemmed | Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data |
| title_short | Existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data |
| title_sort | existence of solutions for unilateral problems associated to some quasilinear anisotropic elliptic equations with measure data |
| topic | unilateral problem nonlinear elliptic equations anisotropic sobolev spaces entropy solutions measure data 35j15 35j62 |
| url | https://doi.org/10.1515/msds-2022-0147 |
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