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(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

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Abstract

We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (\(p>2\)) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric \((p-1)\)-linear term which is resonant as \(x \rightarrow - \infty \), plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zagrafou Campus, Athens, 15780, Greece

    Nikolaos S. Papageorgiou

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

    Calogero Vetro

  3. Department of Energy, Information Engineering and Mathematical Models, University of Palermo, Viale delle Scienze, 90128, 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 Calogero Vetro.

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Papageorgiou, N.S., Vetro, C. & Vetro, F. (p, 2)-Equations with a Crossing Nonlinearity and Concave Terms. Appl Math Optim 81, 221–251 (2020). https://doi.org/10.1007/s00245-018-9482-0

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  • DOI: https://doi.org/10.1007/s00245-018-9482-0

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