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Existence and multiplicity of solutions for second order periodic systems with the p-Laplacian and a nonsmooth potential

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Abstract

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.

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Authors and Affiliations

  1. Institute of Computer Science, Jagiellonian University, ul.Nawojki 11, 30072, Kraków, Poland

    Leszek Gasiński

  2. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Leszek Gasiński
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  2. Nikolaos S. Papageorgiou
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Corresponding author

Correspondence to Leszek Gasiński.

Additional information

Communicated by A. Jüngel.

This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grant nr N201 027 32/1449.

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Gasiński, L., Papageorgiou, N.S. Existence and multiplicity of solutions for second order periodic systems with the p-Laplacian and a nonsmooth potential. Monatsh Math 158, 121–150 (2009). https://doi.org/10.1007/s00605-008-0041-7

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  • DOI: https://doi.org/10.1007/s00605-008-0041-7

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