On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity
Abstract A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of p − 1 $p-1$ . The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-020-01429-x |
| _version_ | 1818043563378737152 |
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| author | Rafik Guefaifia Salah Boulaaras Fares Kamache |
| author_facet | Rafik Guefaifia Salah Boulaaras Fares Kamache |
| author_sort | Rafik Guefaifia |
| collection | DOAJ |
| description | Abstract A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of p − 1 $p-1$ . The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems. An illustrative example is analyzed in order to highlight the obtained result. |
| first_indexed | 2024-12-10T09:04:12Z |
| format | Article |
| id | doaj.art-75f112841b614e8ab02ec6a46d566fae |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-10T09:04:12Z |
| publishDate | 2020-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-75f112841b614e8ab02ec6a46d566fae2022-12-22T01:55:11ZengSpringerOpenBoundary Value Problems1687-27702020-07-012020111510.1186/s13661-020-01429-xOn the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearityRafik Guefaifia0Salah Boulaaras1Fares Kamache2Department of Mathematics, Faculty of Exact Sciences, Larbi Tebessi UniversityDepartment of Mathematics, College of Sciences and Arts, Qassim UniversityDepartment of Mathematics, Faculty of Exact Sciences, Larbi Tebessi UniversityAbstract A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of p − 1 $p-1$ . The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems. An illustrative example is analyzed in order to highlight the obtained result.http://link.springer.com/article/10.1186/s13661-020-01429-xFractional differential equationsRiemann–Liouville fractional derivativesVariational methodsThree solutionsp-Laplacian |
| spellingShingle | Rafik Guefaifia Salah Boulaaras Fares Kamache On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity Boundary Value Problems Fractional differential equations Riemann–Liouville fractional derivatives Variational methods Three solutions p-Laplacian |
| title | On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity |
| title_full | On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity |
| title_fullStr | On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity |
| title_full_unstemmed | On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity |
| title_short | On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity |
| title_sort | on the existence of three solutions of dirichlet fractional systems involving the p laplacian with lipschitz nonlinearity |
| topic | Fractional differential equations Riemann–Liouville fractional derivatives Variational methods Three solutions p-Laplacian |
| url | http://link.springer.com/article/10.1186/s13661-020-01429-x |
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