Boundary value problems for higher order nonlinear ordinary differential systems
type: Item
instance of: scholarly article
title: Boundary value problems for higher order nonlinear ordinary differential systems
zbMATH Open document ID: 0784.34019
author: Shumei Miao
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-10-24T00:00:00Z
review text: The author studies the nonlinear two-point boundary value problem (*) \(x^{(m)}= f(t,x,x',\dots,\) \(x^{(m-1)})\), \(x^{(j)}(0)= A^ j\), \(j=0,1,\dots,m-1\), \(x^{(m-2)}=B\). Here \(m\geq 3\) is a given integer, \(x\) and \(f\) are given \(n\)-dimensional vector functions and \(A^ j\) and \(B\) are given \(n\)-dimensional constant vectors. He presents a new Nagumo condition, which has a simple form similar to the original Nagumo condition, and by means of which the above boundary value problem can be turned into boundary value problems for second order differential systems. Applying Nagumo's theorem and Schauder's fixed point theorem to this system the author obtains an existence theorem for solutions to \((*)\). Three nontrivial examples are discussed.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 417238
zbMATH Keywords: nonlinear two-point boundary value problem
zbMATH Keywords: new Nagumo condition
zbMATH Keywords: Nagumo's theorem
zbMATH Keywords: Schauder's fixed point theorem
zbMATH Keywords: existence
zbMATH Keywords: examples
reviewed by: Manfred Goebel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225920
OpenAlex ID: W2052732765
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DOI: 10.2748/TMJ/1178225920
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description: scientific article; zbMATH DE number 417238