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Degenerate Kirchhoff (p, q)–Fractional Systems with Critical Nonlinearities

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Abstract

This paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p, q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework. The main features and novelty of the paper are the (p, q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non–degenerate.

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Authors and Affiliations

  1. Departament. de Matemática, Universidade Estadual de Campinas, IMECC Rua Sérgio Buarque de Holanda, 651, Campinas, SP CEP 13083-859, Brazil

    Alessio Fiscella

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    Patrizia Pucci

Authors
  1. Alessio Fiscella
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  2. Patrizia Pucci
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Correspondence to Alessio Fiscella.

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Fiscella, A., Pucci, P. Degenerate Kirchhoff (p, q)–Fractional Systems with Critical Nonlinearities. Fract Calc Appl Anal 23, 723–752 (2020). https://doi.org/10.1515/fca-2020-0036

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