Abstract
We are concerned with the existence, uniqueness and global asymptotic behavior of positive continuous solutions to the second-order boundary value problem
1/A(Au')' + a(1)(t)u(sigma 1) + a(2)(t)u(sigma 2) = 0, t is an element of (0,infinity),
subject to the boundary conditions limi(t -> 0+) u(t) = 0, limi(t ->infinity) u(t)/rho(t) = 0, where sigma(1), sigma(2) < 1 and A is a continuous function on [0, infinity) which is positive and differentiable on (0, infinity) such that integral(1)(0) 1/A(t)dt < infinity] andr integral(infinity)(0) 1/A(t) dt = infinity. Here, rho(t) = integral(t)(0) 1/A(s) ds for t > 0 and 01, 02 are nonnegative continuous functions on (0, infinity)) that may be singular at t = 0 and satisfying some appropriate assumptions related to the Karamata regular variation theory. Our approach is based on the sub-supersolution method.