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

Abstract: 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 is its critical exponent provided . Furthermore, we prove that if , then every positive solution of the equations blows up in finite time; whereas for , the equations admit the global positive solutions for some boundary value and some initial data . We also demonstrate that every positive solution of the equations blows up in finite time provided . [Copyright &y& Elsevier]