Existence theorem and global solution for semilinear edge-degenerate hypoelliptic equations

Abstract

In this article, we use the edge-type of Sobolev inequality,Hardy inequlity and Poincare 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 \({\mathcal {H}}^{1,\frac{N}{2}}_{2,0}({\mathbb {E}}).\) Finally, we obtain existence result of global solutions with exponential decay and show the blow-up in finite time of solutions.