Browsing by Author "Hamza , BOUTEBBA"

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    Study of a nonlinear fractional PDEs system
    (20 August 1955 University of Skikda, 2025) Hamza , BOUTEBBA; Hakim , LAKHAL
    Over the past two decades, nonlinear systems of elliptic type involving fractional operators have been extensively studied by numerous researchers in various contexts because they can serve as models for several physical phenomena, and many results on the solvability of these systems have been established. The most interesting aspect has been proving the existence and multiplicity of nontrivial solutions in appropriate fractional Sobolev spaces, using variational methods and critical point theorems. In this regard, the main focus of this thesis is to investigate the concept of existence and multiplicity of nontrivial solutions for classes of nonlinear fractional Schrödinger-Poisson systems and fractional Kirchhoff-Schrödinger-Poisson systems driven by two kinds of fractional operators in appropriate fractional frameworks. In other words, we analyze different classes of these fractional systems under various types of assumptions imposed on the potentials and nonlinearities. To achieve these results, the main techniques employed for the proofs are variational methods based on the mountain pass theorem, the symmetric mountain pass theorem and the fountain theorem.