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.