An existence result for anisotropic quasilinear problems
Analysis of PDEs
2021-02-10 v2
Abstract
We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted {L}aplacian operator with a coefficient that is {locally bounded inside the domain and satisfying certain additional integrability assumptions}. Our main result applies for boundary value problems involving continuous non-linearities having no growth restriction, but provided the existence of a sub and a supersolution is guaranteed. As an application, we present an existence result for a boundary value pro\-blem with a non-linearity satisfying and having sublinear growth at infinity.
Cite
@article{arxiv.2011.13355,
title = {An existence result for anisotropic quasilinear problems},
author = {Oscar Agudelo and Pavel Drábek},
journal= {arXiv preprint arXiv:2011.13355},
year = {2021}
}