In this article, we use the cone Sobolev inequality and the Poincaré inequality to prove the existence theorem for a class of semilinear degenerate hypoelliptic equation on manifolds with conical singularities. In this paper we shall find the existence theorem for the problem (1.1) in cone Sobolev space H 2, 0 1, n 2 (B). Finally, we obtain existence result of global solutions with exponential decay and show the blow-up in finite time of solutions.
