A New proof of Liouville type theorems for a class of semilinear elliptic equations

We study certain typical semilinear elliptic equations in Euclidean space ${\text{bR}}^n$ or on a closed manifold $M$ with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method. Together with suitable integral estimates, some classical Liouville theorems will be reestablished.