The Nonexistence Of Stable Solutions For The Lane-Emden Type Semilinear And Quasilinear Elliptic Systems

In this paper, we investigate the nonexistence of stable solutions for some semi-linear and quasilinear elliptic systems of Lane-Emden type. Such a result is often called the Liouville theorem in the literatures.In chapter 1, we consider the nonexistence of stable solutions for a class of semi-linear elliptic system where N ?3, and min{p, q} > 1.In chapter 2, we consider the nonexistence of stable solutions for a class of quasi-linear elliptic systems where N? 3, min{p,q}> 1,?> 1, ??u = div(|?u|?-2?u).By applying the Moser iteratioan, we are try to deduce a sufficient condition of Joseph-Lundgren type for the nonexistence of stable solutions.