Abstract
The purpose of this paper is to establish an existence and uniqueness theorem for the nonlocal fourth-order nonlinear beam differential equations with a parameter
u((4)) + A(x)u = lambda f(x, u, u ''), 0 < x < 1
subject to the integral boundary conditions:
u(0) = u(1) = integral(1)(0) p(x)u(x)dx, u ''(0) = u ''(1) = integral(1)(0)q(x)u ''(x)dx.
where A is an element of C[0, 1], lambda > 0 is a parameter and p, q is an element of L-1[0, 1].