Existence and nonexistence of global positive solutions for the evolution P-Laplacian equations in exterior domains

This paper deals with the existence and nonexistence of global positive solutions for two evolution P-Laplacian equations in exterior domains with inhomogeneous boundary conditions. We demonstrate that qc=n(p−1)/(n−p)qc=n(p−1)/(n−p) is its critical exponent provided 2n/(n+1)qcq>qc, the equations admit the global positive solutions for some boundary value f(x)f(x) and some initial data u0(x)u0(x). We also demonstrate that every positive solution of the equations blows up in finite time provided n≤pn≤p.