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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-06-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-025-02072-0 |
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| Summary: | 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. |
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| ISSN: | 1687-2770 |