Existence of Solutions to a Nonlocal Boundary Value Problem with Nonlinear Growth

This paper deals with the existence of solutions for the following differential equation: x ''(t) = f(t, x(t),x '(t)), t is an element of (0, 1), subject to the boundary conditions: x(0) = alpha x(xi), x '(1) = integral(1)(0) x ' (s)dg(s), where alpha >= 0, 0 < xi < 1, f : [0, 1] x R-2 -> R is a continuous function, g : [0, 1] -> [0,infinity) is a nondecreasing function with g(0) = 0. Under the resonance condition g(1) = 1, some existence results are given for the boundary value problems. Our method is based upon the coincidence degree theory of Mawhin. We also give an example to illustrate our results.