Positive solution of a singular non-linear elliptic boundary value problem

The singular elliptic boundary value problem: u + g(x)u(alpha) + h(x)u(beta) = 0 in Omega, u > 0 in Omega, u = 0 on partial derivativeOmega is considered in this paper, where alpha epsilon (0, 1), beta > 0, Omega is a bounded region in R-n with a smooth boundary. Under a set of suitable assumptions including that h(x) greater than or equal to 0 in Omega and supp g(-) subset ofsubset of supp h, it is proved that there exists a classic solution u, and when g(x) greater than or equal to 0 (or g(x) less than or equal to 0) in whole Omega, then the solution u is unique. (C) 2003 Elsevier Inc. All rights reserved.