Liouville-type theorems and existence of solutions for quasilinear elliptic problems

J. M. Do Ó; R. F. Freire; E. S. Medeiros

Liouville-type theorems and existence of solutions for quasilinear elliptic problems

Analysis of PDEs 2026-07-02 v1

Authors: J. M. Do Ó , R. F. Freire , E. S. Medeiros

Abstract

This study establishes Liouville-type theorems for indefinite quasilinear elliptic equations in the upper half-space. Additionally, we demonstrate the existence of solutions for this class of problems using the fibering method. Our approach relies on a novel weighted Sobolev embedding developed for the upper half-space.

Keywords

Liouville-type theorems quasilinear elliptic equations upper half-space fibering method weighted Sobolev embedding

Cite

@article{arxiv.2607.02152,
  title  = {Liouville-type theorems and existence of solutions for quasilinear elliptic problems},
  author = {J. M. Do Ó and R. F. Freire and E. S. Medeiros},
  journal= {arXiv preprint arXiv:2607.02152},
  year   = {2026}
}

Comments

29 pages, 3 figures