Existence Results for Nonlinear Boundary Value Problems

In the present paper, we are concerned to prove under some hypothesis the existence of fixed points of the operator L defined on C(I) by Lu(t) = integral(w)(0) G(t ,s)h(s)f(u(s))ds, t is an element of I, omega is an element of {1,infinity}, where the functions f is an element of C([0, infinity);[0, infinity)), h is an element of C(I;[0, infinity)), G is an element of C(I X I) and { I = [0, 1], if omega = 1, I = [0, infinity), if omega = infinity. By using Guo Krasnoselskii fixed point theorem, we establish the existence of at least one fixed point of the operator L.