Mathematical analysis demonstrates Liouville-type theorems and solution existence for quasilinear elliptic equations in the upper half-space, highlighting novel weighted Sobolev embeddings.
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.
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Ó et al. (2026) studied this question.
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