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A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities

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  • Leszek Gasiński
  • Nikolaos Papageorgiou

Abstract

We consider a nonlinear parametric Dirichlet problem driven by the anisotropic p-Laplacian with the combined effects of “concave” and “convex” terms. The “superlinear” nonlinearity need not satisfy the Ambrosetti-Rabinowitz condition. Using variational methods based on the critical point theory and the Ekeland variational principle, we show that for small values of the parameter, the problem has at least two nontrivial smooth positive solutions. Copyright The Author(s) 2013

Suggested Citation

  • Leszek Gasiński & Nikolaos Papageorgiou, 2013. "A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities," Journal of Global Optimization, Springer, vol. 56(4), pages 1347-1360, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1347-1360
    DOI: 10.1007/s10898-011-9841-8
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    References listed on IDEAS

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    1. Alexandru Kristály & Waclaw Marzantowicz & Csaba Varga, 2010. "A non-smooth three critical points theorem with applications in differential inclusions," Journal of Global Optimization, Springer, vol. 46(1), pages 49-62, January.
    2. Kaimin Teng, 2010. "Multiple solutions for semilinear resonant elliptic problems with discontinuous nonlinearities via nonsmooth double linking theorem," Journal of Global Optimization, Springer, vol. 46(1), pages 89-110, January.
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    Cited by:

    1. Leszek Gasiński & Nikolaos S. Papageorgiou, 2020. "Resonant Anisotropic ( p , q )-Equations," Mathematics, MDPI, vol. 8(8), pages 1-21, August.

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