An application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations
type: Item
instance of: scholarly article
title: An application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations
zbMATH Open document ID: 1192.34048
author: Weiguo Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-04-14T00:00:00Z
review text: The present paper is concerned with the existence and uniqueness of a \(2\pi-\) periodic solution of the differential equation \[ u^{(2n)}(t) +\sum^{n-1}_{j=1} (P_j(t) u^{(j)}(t))^{(j)}+ \sum^n_{j=1} A_ju^{(2j-1)}(t) +(-1)^{(n+1)} \bigtriangledown_uf(t,u)=0, \] where \(P_j(t)\in \mathbb{R}^{l\times l},j=1,\dots,n-1,\; A_j\in \mathbb{R}^{l\times l}, j=1,\dots,n\) are symmetric. The approach is to use a global inversion theorem in the author's paper [J. Math. Anal. Appl. 259, No.~1, 157--167 (2001; Zbl 0994.34028)]. Sufficient conditions and examples are provided.
reviewed by: Rong Yuan
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 49J35
zbMATH DE Number: 5543775
zbMATH Keywords: global inversion theorem
zbMATH Keywords: periodic solution
MaRDI profile type: Publication
full work available at URL: j.na.2008.07.044
OpenAlex ID: W1975017818
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DOI: 10.1016/J.NA.2008.07.044
description: scientific article; zbMATH DE number 5543775