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Positive Solutions for Nonlinear Periodic Problems with the Scalar p-Laplacian

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Abstract

We study the existence of positive solutions for a nonlinear periodic problem driven by the scalar p-Laplacian and having a nonsmooth potential. We impose a nonuniform nonresonance condition at + ∞ and a uniform nonresonance condition at 0 + . Using degree theoretic argument based on a fixed point index for multifunctions, we prove the existence of a strict positive solution.

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Authors and Affiliations

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

    Zdzisław Denkowski & Leszek Gasiński

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

    Nikolaos S. Papageorgiou

Authors
  1. Zdzisław Denkowski
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  2. Leszek Gasiński
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  3. Nikolaos S. Papageorgiou
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Corresponding author

Correspondence to Leszek Gasiński.

Additional information

This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants nr. 2 P03A 003 25 and nr. 4 T07A 027 26.

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Denkowski, Z., Gasiński, L. & Papageorgiou, N.S. Positive Solutions for Nonlinear Periodic Problems with the Scalar p-Laplacian. Set-Valued Anal 16, 539–561 (2008). https://doi.org/10.1007/s11228-007-0059-3

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  • DOI: https://doi.org/10.1007/s11228-007-0059-3

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