Abstract
In this article, we study the existence, uniqueness and the asymptotic behavior of a positive classical solution to the semilinear boundary-value problem
-Delta u = a(x)u(sigma) in D,
u vertical bar(partial derivative D) = 0, lim(vertical bar x vertical bar ->infinity) u(x) = 0.
Here D is an unbounded regular domain in R-n(n >= 3) with compact sigma < 1 and the function a is a nonnegative function in C-loc(gamma) (D), 0 < gamma < 1, satisfying an appropriate assumption related to Karamata regular variation theory.