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Nonlinear elliptic problems with superlinear reaction and parametric concave boundary condition

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Abstract

We study parametric nonlinear elliptic boundary value problems driven by the p-Laplacian with convex and concave terms. The convex term appears in the reaction and the concave in the boundary condition (source). We study the existence and nonexistence of positive solutions as the parameter λ > 0 varies. For the semilinear problem (p = 2), we prove a bifurcation type result. Finally, we show the existence of nodal (sign changing) solutions.

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Authors and Affiliations

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

    Nikolaos S. Papageorgiou

  2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Vicenţiu D. Rădulescu

  3. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Vicenţiu D. Rădulescu

Authors
  1. Nikolaos S. Papageorgiou
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  2. Vicenţiu D. Rădulescu
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Corresponding authors

Correspondence to Nikolaos S. Papageorgiou or Vicenţiu D. Rădulescu.

Additional information

V. Rădulescu has been supported through the research grant CNCS-UEFISCDI PCCA-23/2014.

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Papageorgiou, N.S., Rădulescu, V.D. Nonlinear elliptic problems with superlinear reaction and parametric concave boundary condition. Isr. J. Math. 212, 791–824 (2016). https://doi.org/10.1007/s11856-016-1309-6

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  • DOI: https://doi.org/10.1007/s11856-016-1309-6

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