A class of singular perturbation solutions to semilinear equations of fourth order

Abstract

A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied. In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer.

Singularly Perturbed Systems with Diffusion and Time Delay

“…Recently, approximate methods have been developed and refined, including the averaging method, the boundary layer method, the matched asymptotic expansion method, and the multiscale method. Many scholars have done a great deal of work [2][3][4][5][6][7]. However, few of them have studied the nonlinear singularly perturbed with time delay.…”