Singularly perturbed nonlinear boundary value problems on infinite interval
type: Item
instance of: scholarly article
title: Singularly perturbed nonlinear boundary value problems on infinite interval
zbMATH Open document ID: 0686.34058
DOI: 10.1016/0022-0396(89)90128-9
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: The author considers the B.V.P. \(\{ \epsilon y'' = f(x,y,y',\epsilon), y(-\infty,\epsilon) = \infty, y(\infty,\epsilon) = \beta \}\) with the assumption that the degenerate problem \(\{0 = f(x,y,y',0)\}\) has weakly discontinuous solution u, and \(u(-\infty)=\infty\), \(u(\infty)=\beta\). With the use of the usual Nagumo condition, and other inequalities related to differential equations, the author proves the existence and uniqueness of the solution to the problem and obtain the following asymptotic estimate \(| y(x,\epsilon)-u(x)| \leq c,\sqrt{\epsilon}e^{-\mu_ 0| x-x_ 0|}\) \(-\infty <x<\infty\).
reviewed by: Hussain S. Nur
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 34E20
zbMATH DE Number: 4124160
zbMATH Keywords: singularly perturbed nonlinear differential equation
zbMATH Keywords: weakly discontinuous solution
zbMATH Keywords: asymptotic estimate
author: Wei-Li Zhao
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90128-9
OpenAlex ID: W2059264202
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description: scientific article; zbMATH DE number 4124160