Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces
In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential \(V\) on a bounded domain in \(\mathbb{R}^N\) (\(N\geq 3\)) with a smooth boundary. We establish three main results with various assumptions. The first one ass...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2016-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol36/1/art/opuscula_math_3605.pdf |
| _version_ | 1819156777354133504 |
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| author | Ionela-Loredana Stăncuţ Iulia Dorotheea Stîrcu |
| author_facet | Ionela-Loredana Stăncuţ Iulia Dorotheea Stîrcu |
| author_sort | Ionela-Loredana Stăncuţ |
| collection | DOAJ |
| description | In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential \(V\) on a bounded domain in \(\mathbb{R}^N\) (\(N\geq 3\)) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any \(\lambda\gt 0\) is an eigenvalue of our problem. The second theorem states the existence of a constant \(\lambda_{*}\gt 0\) such that any \(\lambda\in(0,\lambda_{*}]\) is an eigenvalue, while the third theorem claims the existence of a constant \(\lambda^{*}\gt 0\) such that every \(\lambda\in[\lambda^{*}, \infty)\) is an eigenvalue of the problem. |
| first_indexed | 2024-12-22T15:58:16Z |
| format | Article |
| id | doaj.art-b3acd5759aa043e6a5da872844483660 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-22T15:58:16Z |
| publishDate | 2016-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-b3acd5759aa043e6a5da8728444836602022-12-21T18:20:45ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742016-01-0136181101http://dx.doi.org/10.7494/OpMath.2016.36.1.813605Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spacesIonela-Loredana Stăncuţ0Iulia Dorotheea Stîrcu1University of Craiova, Department of Mathematics, 200585 Craiova, RomaniaUniversity of Craiova, Department of Mathematics, 200585 Craiova, RomaniaIn this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential \(V\) on a bounded domain in \(\mathbb{R}^N\) (\(N\geq 3\)) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any \(\lambda\gt 0\) is an eigenvalue of our problem. The second theorem states the existence of a constant \(\lambda_{*}\gt 0\) such that any \(\lambda\in(0,\lambda_{*}]\) is an eigenvalue, while the third theorem claims the existence of a constant \(\lambda^{*}\gt 0\) such that every \(\lambda\in[\lambda^{*}, \infty)\) is an eigenvalue of the problem.http://www.opuscula.agh.edu.pl/vol36/1/art/opuscula_math_3605.pdfanisotropic Orlicz-Sobolev spacepotentialcritical pointweak solutioneigenvalue |
| spellingShingle | Ionela-Loredana Stăncuţ Iulia Dorotheea Stîrcu Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces Opuscula Mathematica anisotropic Orlicz-Sobolev space potential critical point weak solution eigenvalue |
| title | Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces |
| title_full | Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces |
| title_fullStr | Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces |
| title_full_unstemmed | Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces |
| title_short | Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces |
| title_sort | eigenvalue problems for anisotropic equations involving a potential on orlicz sobolev type spaces |
| topic | anisotropic Orlicz-Sobolev space potential critical point weak solution eigenvalue |
| url | http://www.opuscula.agh.edu.pl/vol36/1/art/opuscula_math_3605.pdf |
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