(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.