A uniqueness result for a class of infinite semipositone problems with nonlinear boundary conditions

We study positive solutions to the two-point boundary value problem: -u '' = lambda h(t) f (u) : (0, 1) u(0) = 0 u' (1) + c(u1(1))u(1) = 0, where lambda > 0 is a parameter, h is an element of C-1 ((0, 1], (0, infinity)) is a decreasing function, f is an element of C-1 ((0, infinity), R) is an increasing concave function such that lims ->infinity % f (s) = infinity, lims ->infinity f(s)/s = 0, lims -> 0(+) f (s) = -infinity (infinite semipositone) and c is an element of C([0, infinity), (0, infinity)) is an increasing function. For classes of such h and f, we establish the uniqueness of positive solutions for lambda >> 1.