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Existence and Multiplicity of Solutions for Fractional \(\kappa (\xi )\)-Kirchhoff-Type Equation

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Abstract

In this paper, we aim to tackle the questions of existence and multiplicity of solutions to a new class of \(\kappa (\xi )\)-Kirchhoff-type equation utilizing a variational approach. Further, we research the results from the theory of variable exponent Sobolev spaces and from the theory of space \(\psi \)-fractional \({\mathcal {H}}^{\mu ,\nu ;\,\psi }_{\kappa (\xi )}(\Lambda )\). In this sense, we present a few special cases and remark on the outcomes explored.

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Acknowledgements

The authors thank very grateful to the anonymous reviewers for their useful comments that led to improvement of the manuscript. Juan J. Nieto thanks the Agencia Estatal de Investigación (AEI) of Spain under Grant PID2020-113275GB-I00, cofinanced by the European Community fund FEDER, as as well as Xunta de Galicia Grant ED431C 2019/02 for Competitive Reference Research Groups (2019-22).

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Authors and Affiliations

  1. Aerospace Engineering, PPGEA-UEMA, Department of Mathematics, DEMATI-UEMA, São Luís, MA, 65054, Brazil

    J. Vanterler da C. Sousa

  2. Department of Mathematics, Shivaji University, Kolhapur, Maharashtra, 416 004, India

    Kishor D. Kucche

  3. CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain

    Juan J. Nieto

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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., Kucche, K.D. & Nieto, J.J. Existence and Multiplicity of Solutions for Fractional \(\kappa (\xi )\)-Kirchhoff-Type Equation. Qual. Theory Dyn. Syst. 23, 27 (2024). https://doi.org/10.1007/s12346-023-00877-x

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