Browsing by Author "Senoussi Guesmia"

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    Anisotropic non-local problems: asymptotic behaviour and existence results
    (Université de M'sila, 2021) Ahlem Yahiaoui; Senoussi Guesmia; Abdelmouhcene Sengouga
    We deal with anisotropic singular perturbation problems in some weighted spaces of Sobolev type. The perturbed problems are elliptic, semi-linear and non-local. Using a variational approach, we establish the existence of their solutions as critical points of some C1- functionals. Besides, we study the asymptotic behaviour of these solutions with respect to the parameter of perturbation ε and, as ε → 0, we obtain existence results for some non-standard integrodifferential problems. A non-local eigenvalue problem related to the considered problems is also investigated and used to carry out this study.