Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities
Abstract This paper studies a singular anisotropic system of coupled quasilinear elliptic equations. The system features anisotropic diffusion operators with variable exponents p i $p_{i}$ and q i $q_{i}$ , singular terms of the form v − γ 1 $v^{-\gamma _{1}}$ and u − γ 2 $u^{-\gamma _{2}}$ , and no...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02072-0 |
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| _version_ | 1850225804100763648 |
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| author | Seyedeh Atefeh Fallahshams Abdolrahman Razani |
| author_facet | Seyedeh Atefeh Fallahshams Abdolrahman Razani |
| author_sort | Seyedeh Atefeh Fallahshams |
| collection | DOAJ |
| description | Abstract This paper studies a singular anisotropic system of coupled quasilinear elliptic equations. The system features anisotropic diffusion operators with variable exponents p i $p_{i}$ and q i $q_{i}$ , singular terms of the form v − γ 1 $v^{-\gamma _{1}}$ and u − γ 2 $u^{-\gamma _{2}}$ , and nonlinear source terms. By employing variational methods and an approximation problem, we prove the existence of positive solutions under suitable conditions on the nonlinearities. |
| format | Article |
| id | doaj-art-bccc6c37b5bb4e3ebe8ce5e5739d43e9 |
| institution | OA Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-bccc6c37b5bb4e3ebe8ce5e5739d43e92025-08-20T02:05:14ZengSpringerOpenBoundary Value Problems1687-27702025-06-012025111310.1186/s13661-025-02072-0Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearitiesSeyedeh Atefeh Fallahshams0Abdolrahman Razani1Department of Pure Mathematics, Faculty of Science, Imam Khomeini International UniversityDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International UniversityAbstract This paper studies a singular anisotropic system of coupled quasilinear elliptic equations. The system features anisotropic diffusion operators with variable exponents p i $p_{i}$ and q i $q_{i}$ , singular terms of the form v − γ 1 $v^{-\gamma _{1}}$ and u − γ 2 $u^{-\gamma _{2}}$ , and nonlinear source terms. By employing variational methods and an approximation problem, we prove the existence of positive solutions under suitable conditions on the nonlinearities.https://doi.org/10.1186/s13661-025-02072-0Anisotropic ( p , q ) $(p,q)$ -LaplacianSingular problemGlobal continuumVariational method |
| spellingShingle | Seyedeh Atefeh Fallahshams Abdolrahman Razani Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities Boundary Value Problems Anisotropic ( p , q ) $(p,q)$ -Laplacian Singular problem Global continuum Variational method |
| title | Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities |
| title_full | Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities |
| title_fullStr | Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities |
| title_full_unstemmed | Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities |
| title_short | Positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities |
| title_sort | positive solutions to a coupled singular anisotropic system with nonstandard growth and singular nonlinearities |
| topic | Anisotropic ( p , q ) $(p,q)$ -Laplacian Singular problem Global continuum Variational method |
| url | https://doi.org/10.1186/s13661-025-02072-0 |
| work_keys_str_mv | AT seyedehatefehfallahshams positivesolutionstoacoupledsingularanisotropicsystemwithnonstandardgrowthandsingularnonlinearities AT abdolrahmanrazani positivesolutionstoacoupledsingularanisotropicsystemwithnonstandardgrowthandsingularnonlinearities |