Anisotropic non-local problems: asymptotic behaviour and existence results - Ahlem Yahiaoui; Senoussi Guesmia; Abdelmouhcene Sengouga (Université de M'sila, 2021)
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.
Keywords: Anisotropic singular perturbations; non-local problems; eigenvalues and eigenfunctions; critical points AMS SUBJECT