Liouville type theorems for nonlinear elliptic equations on extended Grushin manifolds

Abstract

In this paper, we study two Liouville theorems for nonlinear boundary value problems on extended Grushin manifolds. These problems are closely related to nonlinear fractional Grushin equations. We will prove that these problems do not possess nontrivial positive solution under some assumptions on the nonlinear terms. We use the moving plane method in an integral form to prove our results.