Unique solutions of systems of second-order nonlinear two-point boundary- value problems
type: Item
instance of: scholarly article
title: Unique solutions of systems of second-order nonlinear two-point boundary- value problems
zbMATH Open document ID: 0537.34015
DOI: 10.1016/0377-0427(84)90055-4
author: Robert L. Manicke
published in: Journal of Computational and Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: This paper develops theorems to guarantee the unique existence of systems of boundary value ordinary differential equations of the form: (1) \(\vec y''+\vec f(t,\vec y,\vec y')=0\) with \(\vec y(a)=\vec A\) and \(\vec y(b)=\vec B\) and \(\vec y=(y_ 1,y_ 2,...,y_ n)^ T.\) A Green's function is defined for this system. Then using the contraction mapping theorem on C[a,b] with norm \(\| v\| =\max_{1\leq i\leq n}\{\max_{[a,b]}| v_ i(t)| \}\) conditions are given to show unique existence of solutions of (1).
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 3853511
zbMATH Keywords: Green's function
zbMATH Keywords: contraction mapping theorem
MaRDI profile type: Publication
full work available at URL: 0377-0427(84)90055-4
OpenAlex ID: W2029691088
cites work: Convergence of Successive Approximations for Nonlinear Two-Point Boundary Value Problems
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description: scientific article; zbMATH DE number 3853511