Global structure of positive solutions for nonlocal boundary value problems involving integral conditions

In this paper, we consider the nonlinear eigenvalue problems u '' + lambda h(t)f(u) = 0, 0 < t < 1, u(0) = 0, u(1) = integral(1)(0) u(s)dA(s), where integral(1)(0) u(s)dA(s) is a Stieltjes integral with A nondecreasing and A(t) is not a constant on (0, 1); h is an element of C((0, 1), [0, infinity)) and h(t) (sic) 0 on any subinterval of (0, 1); f is an element of C([0, infinity), [0, infinity)) and f(s) > 0 for s > 0, and f(0) = f(infinity) = 0, f(0) = lim(s -> 0+) f(s)/s, f(infinity) = lim(s ->+infinity)f(s)/s. We investigate the global structure of positive solutions by using global bifurcation techniques. (C) 2009 Elsevier Ltd. All rights reserved.