English

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 pp-{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 f(u)f(u) satisfying f(0)0f(0) \leq 0 and having (p1)(p-1)-sublinear growth at infinity.

Keywords

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}
}
R2 v1 2026-06-23T20:31:55.747Z