Abstract
In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem
-Delta u = a(x)u(sigma) in D,
lim(vertical bar x vertical bar -> 1) u(x) = lim(vertical bar x vertical bar ->infinity) u(x) = 0.
Here D is the complement of the closed unit ball of R-n (n >= 3), sigma < 1 and the function alpha is a nonnegative function in C-loc(gamma)(D), 0 < gamma < 1, satisfying some appropriate assumptions related to Karamata regular variation theory.