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On Noncoercive (p, q)-Equations

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Abstract

We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p − 1)-linear near ±∞ and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

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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. 90123, Palermo, Italy

    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. On Noncoercive (p, q)-Equations. Acta Math Sci 41, 1788–1808 (2021). https://doi.org/10.1007/s10473-021-0524-3

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  • DOI: https://doi.org/10.1007/s10473-021-0524-3

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