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Infinitely many bounded solutions for the p-Laplacian with nonlinear boundary conditions

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Abstract

By applying a method due to Saint Raymond, we prove the existence of infinitely many weak solutions for a quasilinear elliptic partial differential equation, involving the p-Laplacian operator, coupled with a nonlinear boundary condition. Our main assumption is a suitable oscillatory behaviour of the nonlinearity either at infinity or at zero.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Catania, Viale A. Doria 6, 95125, Catania, Italy

    Francesca Faraci & Antonio Iannizzotto

  2. Faculty of Mathematics and Computer Sciences, Babeş-Bolyai University, Str. Kogălniceanu nr. 1, 400084, Cluj-Napoca, Romania

    Csaba Varga

Authors
  1. Francesca Faraci
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  2. Antonio Iannizzotto
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  3. Csaba Varga
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Corresponding author

Correspondence to Francesca Faraci.

Additional information

Communicated by A. Jüngel.

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Faraci, F., Iannizzotto, A. & Varga, C. Infinitely many bounded solutions for the p-Laplacian with nonlinear boundary conditions. Monatsh Math 163, 25–38 (2011). https://doi.org/10.1007/s00605-010-0190-3

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  • DOI: https://doi.org/10.1007/s00605-010-0190-3

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