Abstract
Let Omega be a C-1,C-1-bounded domain in R-n for n >= 2. In this paper, we are concerned with the asymptotic behavior of the unique positive classical solution to the singular boundary-value problem Delta u + a(x)u(-sigma) = 0 in Omega, u(vertical bar partial derivative Omega) = 0, where a sigma >= 0, a is a nonnegative function in C-loc(alpha)(Omega), 0 <alpha < 1 and there exists c > 0 such that 1/c <= a(x)(delta(x))(lambda) Pi(m)(k=1) (Log(k)(omega/delta(x)))(mu k) <= c. Here lambda <= 2, mu(k) is an element of R, omega is a positive constant and delta(x) = dist(x, delta Omega). (C) 2010 Elsevier Inc. All rights reserved.