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Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations

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Abstract

We consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations.

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Acknowledgements

The authors wish to thank the two knowledgeable referees for their corrections and remarks.

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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. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Francesca Vetro

  4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    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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Communicated by Syakila Ahmad.

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Papageorgiou, N.S., Vetro, C. & Vetro, F. Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations. Bull. Malays. Math. Sci. Soc. 43, 2343–2371 (2020). https://doi.org/10.1007/s40840-019-00808-7

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  • DOI: https://doi.org/10.1007/s40840-019-00808-7

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