Abstract
The purpose of this paper is to establish an existence theorem for a system of nonlinear fourth-order differential equations with two parameters {u((4)) + A(x)u = lambda f(x, u, v, u '', v ''), 0 < x < 1,
v((4)) + B(x)v = mu g(x, u, v, u '', v ''), 0 < x < 1,
subject to the coupled integral boundary conditions: {u(0) u'(1) = u ''(1) = 0, u ''(0) = integral(1)(0)p(x)v ''(x)dx,
v(0) = v '''(1) = 0 v ''(0) = integral(1)(0)p(x)i ''(x)dx,
where A , B is an element of C[0 ,1] , p , q is an element of L-1[0 , 1] , lambda > 0 , mu > 0 are two parameters and f, g : [0,1] x [0, infinity) x [0, infinity) x (-infinity, 0) x (-infinity, 0) -> R are two continuous functions satisfy the growth conditions.