Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian
We study the existence and multiplicity of weak solutions for a parametric Neumann problem driven by the p(x)-Laplacian. Under a suitable condition on the behavior of the potential at $0^+$, we obtain an interval such that when a parameter $lambda$ is in this interval, our problem admits at leas...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2013-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/158/abstr.html |
| _version_ | 1819033275666006016 |
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| author | Giuseppina Barletta Antonia Chinni |
| author_facet | Giuseppina Barletta Antonia Chinni |
| author_sort | Giuseppina Barletta |
| collection | DOAJ |
| description | We study the existence and multiplicity of weak solutions for a parametric Neumann problem driven by the p(x)-Laplacian. Under a suitable condition on the behavior of the potential at $0^+$, we obtain an interval such that when a parameter $lambda$ is in this interval, our problem admits at least one nontrivial weak solution. We show the multiplicity of solutions for potentials satisfying also the Ambrosetti-Rabinowitz condition. Moreover, if the right-hand side f satisfies the Ambrosetti-Rabinowitz condition, then we obtain the existence of two nontrivial weak solutions. |
| first_indexed | 2024-12-21T07:15:15Z |
| format | Article |
| id | doaj.art-5fe928e77a9147048d2daa4f5bd362b6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T07:15:15Z |
| publishDate | 2013-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-5fe928e77a9147048d2daa4f5bd362b62022-12-21T19:11:53ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-07-012013158,112Existence of solutions for a Neumann problem involving the $p(x)$-LaplacianGiuseppina BarlettaAntonia ChinniWe study the existence and multiplicity of weak solutions for a parametric Neumann problem driven by the p(x)-Laplacian. Under a suitable condition on the behavior of the potential at $0^+$, we obtain an interval such that when a parameter $lambda$ is in this interval, our problem admits at least one nontrivial weak solution. We show the multiplicity of solutions for potentials satisfying also the Ambrosetti-Rabinowitz condition. Moreover, if the right-hand side f satisfies the Ambrosetti-Rabinowitz condition, then we obtain the existence of two nontrivial weak solutions.http://ejde.math.txstate.edu/Volumes/2013/158/abstr.htmlp(x)-Laplacianvariable exponent Sobolev spaces |
| spellingShingle | Giuseppina Barletta Antonia Chinni Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian Electronic Journal of Differential Equations p(x)-Laplacian variable exponent Sobolev spaces |
| title | Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian |
| title_full | Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian |
| title_fullStr | Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian |
| title_full_unstemmed | Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian |
| title_short | Existence of solutions for a Neumann problem involving the $p(x)$-Laplacian |
| title_sort | existence of solutions for a neumann problem involving the p x laplacian |
| topic | p(x)-Laplacian variable exponent Sobolev spaces |
| url | http://ejde.math.txstate.edu/Volumes/2013/158/abstr.html |
| work_keys_str_mv | AT giuseppinabarletta existenceofsolutionsforaneumannprobleminvolvingthepxlaplacian AT antoniachinni existenceofsolutionsforaneumannprobleminvolvingthepxlaplacian |