Abstract
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional approximation is constructed. Applications regarding nonhomogeneous Dirichlet problems and equations with convolution are given by choosing an adequate intrinsic operator.
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Acknowledgements
The authors thank Luiz Fernando Faria and Anderson Luiz de Albuquerque Araujo for useful conmments.
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The authors take part in the project Special Visiting Researcher - FAPEMIG CEX APQ 04528/22.
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Communicated by Liliane Maia.
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Medeiros, A.H.S., Motreanu, D. A problem involving competing and intrinsic operators. São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-024-00405-y
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DOI: https://doi.org/10.1007/s40863-024-00405-y
Keywords
- p-Laplacian
- Competing operator
- Convection
- Generalized solution
- Approximation
- Nonhomogeneous boundary condition
- Convolution