An existence of an isolated solution to nonlinear two-point boundary value problem with parameter
type: Item
instance of: scholarly article
title: An existence of an isolated solution to nonlinear two-point boundary value problem with parameter
zbMATH Open document ID: 1492.34019
DOI: 10.1134/S199508022103015X
author: Yanyan Li
published in: Lobachevskii Journal of Mathematics
publication date: 2021-05-20T00:00:00Z
review text: The authors use the parametrization method to study the nonlinear two-point boundary value problem \[ x' = f(t, x, \mu), t \in (0, T), x \in \mathbb{R}^n, \mu \in \mathbb{R}^m, g(\mu, x(0), x(T)) = 0, \] where \(f: [0, T]\times \mathbb{R}^n \times \mathbb{R}^m\to \mathbb{R}^n\), \(g: \mathbb{R}^m \times \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}^{n+m}\) are continuous. The method consists in partition of the interval apart, the introduction of additional parameters and reducing the original problem to the equivalent multi-point boundary value problem with parameters. The algorithms for finding a solution to an equivalent boundary value problem are constructed. The conditions for convergence of the algorithms that ensure the solvability of nonlinear two-point boundary value problem with parameter are obtained.
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 7350136
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: solvability
zbMATH Keywords: parametrization method
zbMATH Keywords: nonlinear two-point boundary value problem with parameter
zbMATH Keywords: isolated solution
reviewed by: Ruyun Ma
MaRDI profile type: Publication
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full work available at URL: s199508022103015x
OpenAlex ID: W3157775288
description: scientific article; zbMATH DE number 7350136