Abstract
We study the boundary-value problem
1/A(t)(A(t)u'(t))' = lambda f(t, u(t)) t is an element of (0, infinity),
lim(t -> 0+) A(t)u'(t) = -a <= 0, lim(t ->infinity) u(t) = b > 0,
where lambda >= 0 and f is nonnegative continuous and nondecreasing with respect to the second variable. Under some assumptions on the nonlinearity f, we prove the existence of a positive solution for A sufficiently small. Our approach is based on the Schauder fixed point theorem.