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Singular Double Phase Problems with Convection

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Abstract

We consider a nonlinear Dirichlet problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

  2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Calogero Vetro

  3. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Francesca Vetro

  4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Francesca Vetro

Authors
  1. Nikolaos S. Papageorgiou
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  2. Calogero Vetro
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  3. Francesca Vetro
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Correspondence to Francesca Vetro.

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Papageorgiou, N.S., Vetro, C. & Vetro, F. Singular Double Phase Problems with Convection. Acta Appl Math 170, 947–962 (2020). https://doi.org/10.1007/s10440-020-00364-4

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  • DOI: https://doi.org/10.1007/s10440-020-00364-4

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