Approximation of Multi-Region Inner Layer Solutions for Second-Order Weakly Nonlinear Singularly Perturbed Problems with Advance and Delay

Abstract: The paper studies a class of weakly nonlinear singular perturbation problems with bothadvance and delay. We use the Vasil’eva boundary layer function method, the “step-by-step”method, and the sewing method to not only construct a uniformly valid asymptotic expansion forthe solution of the original problem, but also to prove the existence of a smooth solution in theinner layer. Finally, examples are given to demonstrate the effectiveness of the constructed resultsin this paper.