In this paper we consider the operator equation in a real Banach space E with cone P: where A = KF; here K is a e-positive, e-continuous and completely continuous operator, and F is a strictly increasing and continuous operator which is Frechet differentiable at θ. Under certain conditions, we show that the operator equation has at least three solutions x1, x2, x3 such that x1 ∈ P, x2 ∈ (−P), x3 ∈ E\(P ∪ (−P)). Now since the third solution x3 ∈ E\(P ∪ (−P)), we call it a sign-changing solution. As an application of the main results, we investigate the existence of sign-changing solutions for some three-point boundary value problem.