This research reveals nonexistence of positive solutions for semilinear inequalities on pseudo-Hermitian manifolds, suggesting implications for mathematical frameworks.
In this paper, we study the semilinear elliptic equation and inequality on pseudo-Hermitian manifolds. In particular, we first obtain a Liouville theorem for the equation Δb u+F(u)=0 based on a generalized Jerison-Lee's formula. Next, we prove the nonexistence of a positive solution to the inequality Δb u+F(u)≤ 0 under the volume estimate.
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Biqiang Zhao (2025) studied this question.
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