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

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.

29 pages, 3 figures