Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases
Abstract
We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient conditions for the existence of at least one or two non-negative solutions. Our analysis considers the cases when the reaction has either a sublinear or a linear growth. In the sublinear case, we also prove a nonexistence property. The proofs combine energy estimates and variational methods. In particular, the monotonicity trick is applied in order to overcome the lack of a priori bounds on the Palais-Smale sequences.
Cite
@article{arxiv.2002.06813,
title = {Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases},
author = {Louis Jeanjean and Vicentiu D. Radulescu},
journal= {arXiv preprint arXiv:2002.06813},
year = {2022}
}
Comments
This version is the final one, corresponding to the paper now published in Journal d'Analyse Math\'ematique