Abstract
In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem:
-Delta u = q(x)u(sigma) in Omega, u(vertical bar partial derivative Omega) = 0.
Here Omega is an annulus in R-n, n >= 3, sigma < 1 and q is a positive function in C-loc(gamma)(Omega), 0 < gamma < 1, satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.