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Existence of Solutions for a Singular Double Phase Problem Involving a \(\psi \)-Hilfer Fractional Operator Via Nehari Manifold

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Abstract

In this present paper, we investigate a new class of singular double phase p-Laplacian equation problems with a \(\psi \)-Hilfer fractional operator combined from a parametric term. Motivated by the fibering method using the Nehari manifold, we discuss the existence of at least two weak solutions to such problems when the parameter is small enough. Before attacking the main contribution, we discuss some results involving the energy functional and the Nehari manifold.

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Acknowledgements

All authors’ contributions to this manuscript are the same. All authors read and approved the final manuscript. We are very grateful to the anonymous reviewers for their useful comments that led to improvement of the manuscript.

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Authors and Affiliations

  1. Center for Mathematics, Computing and Cognition, Federal University of ABC, Avenida dos Estados, 5001, Bairro Bangu, Santo André, SP, 09.210-580, Brazil

    J. Vanterler da C. Sousa

  2. Faculty of Exact Sciences and Technology, FACET, UFGD, Dourados, MS, 79804-970, Brazil

    Karla B. Lima

  3. Center of Sciences and Technology, Federal University of Cariri, Juazeiro do Norte, Brazil

    Leandro S. Tavares

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  1. J. Vanterler da C. Sousa
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Correspondence to J. Vanterler da C. Sousa.

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Sousa, J.V.d.C., Lima, K.B. & Tavares, L.S. Existence of Solutions for a Singular Double Phase Problem Involving a \(\psi \)-Hilfer Fractional Operator Via Nehari Manifold. Qual. Theory Dyn. Syst. 22, 94 (2023). https://doi.org/10.1007/s12346-023-00794-z

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