Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation

We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equation x ''(t) = f(t,x(phi(t))), t is an element of (0,1), with the nonlocal condition Sigma(m)(k=1) a(k)(x)(tau(k)) = x(0), x'(0) + Sigma(n)(j=1) (eta(j)) = x(1), where tau(k) is an element of (a,d) subset of (0,1), eta(j) is an element of (c,e) subset of (0,1), and x(0), x(1) > 0. As an application the integral and the nonlocal conditions integral(d)(a) x(t)dt = x(0), x'(0) + x(e) - x(c) = x(1) will be considered.