A fourth-order iterative boundary value problem with Lidstone boundary conditions

Abstract

. Let m (cid:2) 2 and a > 0. We consider the existence and uniqueness of solutions to the fourth-order iterative boundary value problem solutions satisfying Lidstone Here the iterative functions are de fi ned by x [ 2 ] ( t ) = x ( x ( t )) and for j = 3 ,... m , x [ j ( t ) = x ( x [ j − 1 ] ( t )) . The main tool employed to establish our results is the Schauder fi xed point theorem.