Third-order nonlinear singularly perturbed boundary value problem.
type: Item
instance of: scholarly article
title: Third-order nonlinear singularly perturbed boundary value problem.
zbMATH Open document ID: 1036.34028
DOI: 10.1007/BF02437651
author: Guocan Wang
author: Li Jin
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2003-06-18T00:00:00Z
review text: The authors study the following boundary value problems with the small parameter \(\varepsilon>0\) \[ \varepsilon x'''=f(t,x,x',\varepsilon), \] \[ \begin{cases} x(0)=A,\;g(x'(0),\;x'(1))=0,\\ h(x'(0),\;x'(1),\;x''(0),\;x''(1))=0,\end{cases} \] where \(g\) and \(h\) are continuous functions of their arguments under some additional restrictions. In particular, the following boundary conditions \[ x(0)=A,\;x'(0)=x'(1),\;x''(0)=x''(1), \] are considered. Specific upper and lower solutions are constructed, and the existence of solutions are shown and asymptotic estimates on solutions under suitable conditions are obtained. An example illustrating the applicability of the main results is given.
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1880779
zbMATH Keywords: third-order boundary value problem
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: existence and asymptotic estimates
reviewed by: G. Jaiani
MaRDI profile type: Publication
cites work: Q3808496
cites work: Existence of solutions to boundary value problems for second order differential equations
description: scientific article; zbMATH DE number 1880779