Internal Layers for a Singularly Perturbed Second-Order Quasilinear Differential Equation with Discontinuous Right-Hand Side

Mingkang Ni; Yafei Pang; N. T. Levashova; O. A. Nikolaeva

doi:10.1134/S0012266117120059

Internal Layers for a Singularly Perturbed Second-Order Quasilinear Differential Equation with Discontinuous Right-Hand Side

Authors: Ni M.¹, Pang Y.¹, Levashova N.T.², Nikolaeva O.A.²
Affiliations:
1. East China Normal University
2. Lomonosov Moscow State University
Issue: Vol 53, No 12 (2017)
Pages: 1567-1577
Section: Ordinary Differential Equations
URL: https://journal-vniispk.ru/0012-2661/article/view/154642
DOI: https://doi.org/10.1134/S0012266117120059
ID: 154642

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Abstract

A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.