Positive solutions of a semilinear elliptic equation with singular nonlinearity

摘要

This paper is devoted to the study of positive solutions of the semilinear elliptic equation Delta u + K(vertical bar x vertical bar)u(-P) = 0, x epsilon R-n with n >= 3 and p > 0. Asymptotic behaviours of sky states and uniqueness of singular sky states are obtained via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has infinitely many positive solutions with fast growth. (c) 2005 Elsevier Inc. All rights reserved.