Existence and uniqueness of solutions for a second-order iterative boundary-value problem

Abstract

<p>We consider the existence and uniqueness of solutions to the second-order iterative boundary-value problem</p> <pre>x″(t) = ƒ(t, x(t), x^[2](t)), α ≤ t ≤ b,</pre> <p>where x^[2](t) = x(x(t)), with solutions satisfying one of the boundary conditions x(α) = α, x(b) = b or x(α) = b, x(b) = α. The main tool employed to establish our results is the Schauder fixed point theorem.</p>