Formation of boundary layers for singularly perturbed fourth-order ordinary differential equations with the Lidstone boundary conditions

In this paper we concentrate on the aspect of the boundary layer phenomenon that represents a typical asymptotic behavior mode of singularly perturbed systems at the endpoints of the considered interval. We provide a detailed analysis of this phenomenon for the nonlinear fourth-order ordinary differential equations subject to the Lidstone boundary conditions by an analysis of the integral equation associated with an original boundary value problem. (C) 2016 Elsevier Inc. All rights reserved.