This analysis reveals optimal conditions for degenerate elliptic equations, showing the existence of bounded solutions. Findings indicate implications for drift terms and potential behavior.
We obtain Liouville type theorems for degenerate elliptic equations with a drift term and a potential. The diffusion is governed by Hörmander operators. We show that the conditions imposed on the coefficients of the operator are optimal. Indeed, when they fail we prove that infinitely many bounded solutions exist.
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Biagi et al. (2025) studied this question.
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