  In this paper, we study Pohozaev identities, Kelvin transformation and their
applications of semilinear Grushin equation. First, we establish two Pohozaev
identities generated from translations and determine the location of the
concentration point for solution of a kind of Grushin equation by such
identities. Next, we establish Pohozaev identity generated from scaling and
prove the nonexistence of nontrivial solutions of another kind of Grushin
equation by such identity. Finally, we provide the change of Grushin operator
by Kelvin transformation and obtain the decay rate of solution at infinity for
a critical Grushin equation by Kelvin transformation.
