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 q(c) = n(p - 1)1(n - p) is its critical exponent provided 2n/(n + 1) < p < n. Furthermore, we prove that if max{1, p - } < q <= q(c), then every positive solution of the equations blows up in finite time; whereas for q > q(c), the equations admit the global positive solutions for some boundary value f (x) and some initial data u(o)(x). We also demonstrate that every positive solution of the equations blows up in finite time provided n <= p. (c) 2006 Elsevier Ltd. All rights reserved.