Liouville type results for semilinear elliptic equation and inequality on Sasakian manifolds

Abstract

In this paper, we study the semilinear elliptic equation and inequality on Sasakian manifolds. First, we obtain Liouville theorems for the equation ${\Delta }_{b}u+F(u)=0$ based on a generalized Jerison-Lee's formula. Next, we prove the nonexistence of positive weak solutions to the inequality ${\Delta }_{b}u+F(u)\le 0$ under the volume estimate.

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