This article is dedicated to study of the initial-boundary value problem of edge pseudo-hyperbolic system with damping term on the manifold with edge singularity. First, we will discuss about the invariance of solution set of a class of edge degenerate pseudo-hyperbolic equations on the edge Sobolev spaces. Then, by using a family of modified potential wells and concavity methods, it is obtained existence and nonexistence results of global solutions with exponential decay and is shown the blow-up in finite time of solutions on themanifold with edge singularities
