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  • Problèmes de valeurs propres pour des opérateurs ▫$\vec{\rho}$▫-multivoques : thèse pour l'obtention du Grade de Docteur de l'Université de Poitiers
    Chrayteh, Houssam
    The aim of our research is to study the existence and regularity of solutions for eigenvalue problems involving a ▫$\vec{\rho}$▫-multivoque operator ▫$A \colon\mathbf{V} \to \mathcal{P}({\mathbf ... V}^\ast)$▫ on a smooth domain ▫$\Omega\subset {\mathbb R}^N$▫. Through ▫$\mathcal{N}$▫-functions, we construct a ▫$\vec{\rho}$▫-multivoque Leray-Lions ``strongly monotonic'' operator on an anisotropic Orlicz-Sobolev space. We note that the theoretical formulation of problems related to such operator is essentially based on the notion of Clarke subdifferential. For this reason, we introduce new variational methods that match the resolution of these issues in the ``subcritical'' case where compactness plays an important role and ``critical'' case when we lose compactness. Various applications are given to illustrate our abstract results, for example, an anisotropic operator with variable exponents and an operator with a Hardy type weight.
    Type of material - dissertation ; adult, serious
    Publication and manufacture - Poitiers : [H. Chrayteh], 2012
    Language - french
    COBISS.SI-ID - 16279385

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