Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions
In this paper we study the existence of at least two nontrivial solutions for the nonlinear problem p-Laplacian, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediar...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2016-10-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/23645 |
| _version_ | 1819230874035552256 |
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| author | Mohammed Berrajaa Omar Chakrone Fatiha Diyer Okacha Diyer |
| author_facet | Mohammed Berrajaa Omar Chakrone Fatiha Diyer Okacha Diyer |
| author_sort | Mohammed Berrajaa |
| collection | DOAJ |
| description | In this paper we study the existence of at least two nontrivial solutions for the nonlinear problem p-Laplacian, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediary eigenvalue problem by the minimization method. In fact, in some sense, we establish the non-resonance below the first eigenvalues of nonlinear Steklov-Robin. |
| first_indexed | 2024-12-23T11:36:00Z |
| format | Article |
| id | doaj.art-3a40c3f1d28949b49a0199b144ff63bb |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-23T11:36:00Z |
| publishDate | 2016-10-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-3a40c3f1d28949b49a0199b144ff63bb2022-12-21T17:48:39ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882016-10-01341657410.5269/bspm.v34i1.2364511592Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditionsMohammed Berrajaa0Omar Chakrone1Fatiha Diyer2Okacha Diyer3University Mohamed I Faculty of sciences Department of MathematicsUniversity Mohamed I Faculty of sciences Department of MathematicsUniversity Mohamed I Faculty of sciences Department of MathematicsUniversity Mohamed I Faculty of sciences Department of MathematicsIn this paper we study the existence of at least two nontrivial solutions for the nonlinear problem p-Laplacian, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediary eigenvalue problem by the minimization method. In fact, in some sense, we establish the non-resonance below the first eigenvalues of nonlinear Steklov-Robin.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/23645Eigenproblemp-Laplacian operatorvariational methodnon-resonance problems |
| spellingShingle | Mohammed Berrajaa Omar Chakrone Fatiha Diyer Okacha Diyer Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions Boletim da Sociedade Paranaense de Matemática Eigenproblem p-Laplacian operator variational method non-resonance problems |
| title | Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions |
| title_full | Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions |
| title_fullStr | Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions |
| title_full_unstemmed | Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions |
| title_short | Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions |
| title_sort | multiple solutions for p laplacian eigenproblem with nonlinear boundary conditions |
| topic | Eigenproblem p-Laplacian operator variational method non-resonance problems |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/23645 |
| work_keys_str_mv | AT mohammedberrajaa multiplesolutionsforplaplacianeigenproblemwithnonlinearboundaryconditions AT omarchakrone multiplesolutionsforplaplacianeigenproblemwithnonlinearboundaryconditions AT fatihadiyer multiplesolutionsforplaplacianeigenproblemwithnonlinearboundaryconditions AT okachadiyer multiplesolutionsforplaplacianeigenproblemwithnonlinearboundaryconditions |