Anisotropic non-local problems: asymptotic behaviour and existence results
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
Université de M'sila
Abstract
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.
Description
Keywords
Anisotropic singular perturbations; non-local problems; eigenvalues and eigenfunctions; critical points AMS SUBJECT