Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator
We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and th...
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| Format: | Article |
| Language: | English |
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University of Szeged
2018-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6121 |
| _version_ | 1797830602722902016 |
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| author | Calogero Vetro |
| author_facet | Calogero Vetro |
| author_sort | Calogero Vetro |
| collection | DOAJ |
| description | We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory. |
| first_indexed | 2024-04-09T13:38:44Z |
| format | Article |
| id | doaj.art-c3d03a4dde8f4b55becacb73ecf6232e |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:44Z |
| publishDate | 2018-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-c3d03a4dde8f4b55becacb73ecf6232e2023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-01-0120179811010.14232/ejqtde.2017.1.986121Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operatorCalogero Vetro0University of Palermo, Palermo, ItalyWe prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6121dirichlet boundary value problem$p(x)$-laplacian-like operatorvariable exponent sobolev space |
| spellingShingle | Calogero Vetro Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator Electronic Journal of Qualitative Theory of Differential Equations dirichlet boundary value problem $p(x)$-laplacian-like operator variable exponent sobolev space |
| title | Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator |
| title_full | Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator |
| title_fullStr | Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator |
| title_full_unstemmed | Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator |
| title_short | Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator |
| title_sort | weak solutions to dirichlet boundary value problem driven by p x laplacian like operator |
| topic | dirichlet boundary value problem $p(x)$-laplacian-like operator variable exponent sobolev space |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6121 |
| work_keys_str_mv | AT calogerovetro weaksolutionstodirichletboundaryvalueproblemdrivenbypxlaplacianlikeoperator |