Abstract
We prove the existence and uniqueness, and study the global behavior of a positive continuous solution to the superlinear second-order differential equation
1/A(t) (A(t)u'(t))' = u(t)g(t, u(t)), t is an element of (0, infinity),
u(0) = a, lim(t ->infinity) u(t)/rho(t) = b,
where a, b are nonnegative constants such that a + b > 0, A is a continuous function on [0, infinity), positive and continuously differentiable on (0, infinity) such that 1/A is integrable on [0, 1] and integral(infinity)(0) 1/A(t) dt = infinity. Here rho(t) = integral(t)(0) 1/A(s) ds, for t >= 0 and g(t, s) is a nonnegative continuous function satisfying suitable integrability condition. Our Approach is based on estimates of the Green's function and a perturbation argument. Finally two illustrative examples are given.