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Qualitative Properties of Eigenvectors Related to Multivalued Operators and some Existence Results

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Abstract

In this work, we study a class of nonlinear eigenvalue problems related to fully discontinuous operators. In particular, we prove the existence of a critical point for two distinct problems. Connected with this problem, we also study a minimization problem with constraint, and we investigate the existence of solutions for a resonant case near zero. Moreover, we give some estimates and qualitative properties of solutions by using the relative rearrangement theory.

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Acknowledgements

The author wishes to thank Professor Jean-Michel Rakotoson for many stimulating discussions and useful comments on the subject of the paper and he wishes to thank Dr. Madalina Petcu for the English corrections.

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Authors and Affiliations

  1. UMR 7348 CNRS, Laboratoire de Mathématiques et Applications, Université de Poitiers, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, BP30179, 86962, Futuroscope, Chasseneuil Cedex, France

    Houssam Chrayteh

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  1. Houssam Chrayteh
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Correspondence to Houssam Chrayteh.

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Communicated by Michel Théra.

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Chrayteh, H. Qualitative Properties of Eigenvectors Related to Multivalued Operators and some Existence Results. J Optim Theory Appl 155, 507–533 (2012). https://doi.org/10.1007/s10957-012-0064-z

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