Abstract
We prove the existence of positive solutions for a system of quasilinear equations driven by \(p_i\)-Laplacian operators, with Dirichlet boundary conditions, variable exponents, convection terms, and depending on two parameters. No upper bound on the variable exponents, neither in u nor in \(\nabla u\), is imposed. It is for the first time when such systems are investigated. The range of solvability for the involved parameters is explicitly determined. Our approach relies on a version of sub-supersolution method for systems that is adapted to the specific character of our problem.
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This work was partially supported by FAPEMIG APQ-04528-22. Anderson de Araujo was partially supported by CNPq. Luiz F.O Faria was partially supported by CNPq.
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Araujo, A.d., Faria, L. & Motreanu, D. Quasilinear Systems with Unbounded Variable Exponents and Convection Terms. Bull Braz Math Soc, New Series 55, 17 (2024). https://doi.org/10.1007/s00574-024-00391-x
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DOI: https://doi.org/10.1007/s00574-024-00391-x
Keywords
- Dirichlet problem for systems
- Sub-supersolution method
- Supercritical growth
- Convection term
- Variable exponents.