Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction
We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction f(z,ζ), whose primitive f(z,ζ) is p-superlinear near ±∞, but need not satisfy the usual in such cases, the Ambrosetti-Rabinowitz condition. Using a combination of var...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/918271 |
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| author | Leszek Gasiński Nikolaos S. Papageorgiou |
| author_facet | Leszek Gasiński Nikolaos S. Papageorgiou |
| author_sort | Leszek Gasiński |
| collection | DOAJ |
| description | We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction f(z,ζ), whose primitive f(z,ζ) is p-superlinear near ±∞, but need not satisfy the usual in such cases, the Ambrosetti-Rabinowitz condition. Using a combination of variational methods with the Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions. Our result unifies the study of “superlinear” equations monitored by some differential operators of interest like the p-Laplacian, the (p,q)-Laplacian, and the p-generalized mean curvature operator. |
| format | Article |
| id | doaj-art-ec2bec6bf62c405dac3364dbd9a691aa |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ec2bec6bf62c405dac3364dbd9a691aa2025-08-20T03:21:23ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/918271918271Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear ReactionLeszek Gasiński0Nikolaos S. Papageorgiou1Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza Street 6, 30-348 Kraków, PolandDepartment of Mathematics, National Technical University, Zografou Campus, 15780 Athens, GreeceWe consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction f(z,ζ), whose primitive f(z,ζ) is p-superlinear near ±∞, but need not satisfy the usual in such cases, the Ambrosetti-Rabinowitz condition. Using a combination of variational methods with the Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions. Our result unifies the study of “superlinear” equations monitored by some differential operators of interest like the p-Laplacian, the (p,q)-Laplacian, and the p-generalized mean curvature operator.http://dx.doi.org/10.1155/2012/918271 |
| spellingShingle | Leszek Gasiński Nikolaos S. Papageorgiou Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction Abstract and Applied Analysis |
| title | Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction |
| title_full | Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction |
| title_fullStr | Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction |
| title_full_unstemmed | Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction |
| title_short | Nonhomogeneous Nonlinear Dirichlet Problems with a p-Superlinear Reaction |
| title_sort | nonhomogeneous nonlinear dirichlet problems with a p superlinear reaction |
| url | http://dx.doi.org/10.1155/2012/918271 |
| work_keys_str_mv | AT leszekgasinski nonhomogeneousnonlineardirichletproblemswithapsuperlinearreaction AT nikolaosspapageorgiou nonhomogeneousnonlineardirichletproblemswithapsuperlinearreaction |