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Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

Author

Listed:
  • Nikolaos S. Papageorgiou

    (National Technical University)

  • Vicenţiu D. Rădulescu

    (King Abdulaziz University
    University of Craiova)

  • Dušan D. Repovš

    (University of Ljubljana)

Abstract

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).

Suggested Citation

  • Nikolaos S. Papageorgiou & Vicenţiu D. Rădulescu & Dušan D. Repovš, 2017. "Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 293-323, November.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:2:d:10.1007_s10957-017-1173-5
    DOI: 10.1007/s10957-017-1173-5
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    Cited by:

    1. Ghasem A. Afrouzi & Martin Bohner & Giuseppe Caristi & Shapour Heidarkhani & Shahin Moradi, 2018. "An Existence Result for Impulsive Multi-point Boundary Value Systems Using a Local Minimization Principle," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 1-20, April.
    2. Yi Cheng & Donal O'Regan, 2021. "Characteristic of solutions for non‐local fractional p(x)‐Laplacian with multi‐valued nonlinear perturbations," Mathematische Nachrichten, Wiley Blackwell, vol. 294(7), pages 1311-1332, July.

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