In this article, we use the edge-type of Sobolev inequality,Hardy inequlity and 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 H1,N22,0(E).H2,01,N2(E). Finally, we obtain existence result of global solutions with exponential decay and show the blow-up in finite time of solutions.
