Existence of solutions for a resonant Steklov Problem
In this paper, we prove the existence of weak solutions to the problem △_p u = 0 in Ω, |∇u|^{p−2} ∂_ν u = λ_1 m(x)|u|^{p−2}u + f(x, u) − h on ∂Ω, where Ω is a bounded domain in RN (N ≥ 2), m ∈ L^q(∂Ω) is a weight, λ_1 is the first positive eigenvalue for the eigenvalue Steklov problem △pu = 0 in Ω an...
| Glavni autori: | , , , |
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| Format: | Članak |
| Jezik: | English |
| Izdano: |
Sociedade Brasileira de Matemática
2009-07-01
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| Serija: | Boletim da Sociedade Paranaense de Matemática |
| Teme: | |
| Online pristup: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/9070/5274 |
| _version_ | 1830310047805079552 |
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| author | Belhadj KARIM Omar CHAKRONE Aomar ANANE Abdellah ZEROUALI |
| author_facet | Belhadj KARIM Omar CHAKRONE Aomar ANANE Abdellah ZEROUALI |
| author_sort | Belhadj KARIM |
| collection | DOAJ |
| description | In this paper, we prove the existence of weak solutions to the problem △_p u = 0 in Ω, |∇u|^{p−2} ∂_ν u = λ_1 m(x)|u|^{p−2}u + f(x, u) − h on ∂Ω, where Ω is a bounded domain in RN (N ≥ 2), m ∈ L^q(∂Ω) is a weight, λ_1 is the first positive eigenvalue for the eigenvalue Steklov problem △pu = 0 in Ω and |∇u|^{p−2} ∂_ν u=λ m(x)|u|^{p−2}u on ∂Ω. f and h are functions that satisfy some conditions. |
| first_indexed | 2024-12-19T11:17:58Z |
| format | Article |
| id | doaj.art-bbae9fc8cda1444aaafd692e1a53e18d |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-19T11:17:58Z |
| publishDate | 2009-07-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-bbae9fc8cda1444aaafd692e1a53e18d2022-12-21T20:23:59ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882009-07-012718590Existence of solutions for a resonant Steklov ProblemBelhadj KARIMOmar CHAKRONEAomar ANANEAbdellah ZEROUALIIn this paper, we prove the existence of weak solutions to the problem △_p u = 0 in Ω, |∇u|^{p−2} ∂_ν u = λ_1 m(x)|u|^{p−2}u + f(x, u) − h on ∂Ω, where Ω is a bounded domain in RN (N ≥ 2), m ∈ L^q(∂Ω) is a weight, λ_1 is the first positive eigenvalue for the eigenvalue Steklov problem △pu = 0 in Ω and |∇u|^{p−2} ∂_ν u=λ m(x)|u|^{p−2}u on ∂Ω. f and h are functions that satisfy some conditions.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/9070/5274Steklov problemWeightsLandesman-Lazer conditionsPalais–Smale conditions. |
| spellingShingle | Belhadj KARIM Omar CHAKRONE Aomar ANANE Abdellah ZEROUALI Existence of solutions for a resonant Steklov Problem Boletim da Sociedade Paranaense de Matemática Steklov problem Weights Landesman-Lazer conditions Palais–Smale conditions. |
| title | Existence of solutions for a resonant Steklov Problem |
| title_full | Existence of solutions for a resonant Steklov Problem |
| title_fullStr | Existence of solutions for a resonant Steklov Problem |
| title_full_unstemmed | Existence of solutions for a resonant Steklov Problem |
| title_short | Existence of solutions for a resonant Steklov Problem |
| title_sort | existence of solutions for a resonant steklov problem |
| topic | Steklov problem Weights Landesman-Lazer conditions Palais–Smale conditions. |
| url | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/9070/5274 |
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