Boundedness of solutions of nonlinear differential delay equations with positive Green functions and the Aizerman-Myshkis problem
type: Item
instance of: scholarly article
title: Boundedness of solutions of nonlinear differential delay equations with positive Green functions and the Aizerman-Myshkis problem
zbMATH Open document ID: 1014.34063
DOI: 10.1016/S0362-546X(01)00725-8
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: Here, the author investigates the scalar equation \[ x^{(n)}(t)+\sum\limits_{k=0}^{n-1}\int_{0}^{\eta}x^{(k)}(t-\tau) dr_k(\tau)= N(D)F(t,x_t)\quad t>0, \] where \(r_k\), \(k=0,\ldots,n-1\), are bounded nondecreasing functions defined on a finite segment \([0,\eta], D\equiv d/dt\), \(N(\lambda)=1+\cdots+b_m\lambda^m\), \(b_k= \text{const}\), \(k=1,\ldots,m<n\), is a polynomial and \(x_t(\theta)=x(t+\theta)\) with \(\theta\in [-\eta,0]\), \(F\in \mathbb{R}_+\times \mathbb{C}[-\eta,0]\). He establishes explicit conditions for solution boundedness and absolute stability of equation (1) with the positive Green function (the fundamental solution, the impulse function).
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K12
zbMATH DE Number: 1787984
zbMATH Keywords: nonlinear equations with delay
zbMATH Keywords: positive Green function
zbMATH Keywords: boundedness of solutions
zbMATH Keywords: absolute stability
zbMATH Keywords: the Aizerman-Myshkis problem
author: Michael I. Gil'
MaRDI profile type: Publication
cites work: Q4001772
cites work: Stability and periodic solutions of ordinary and functional differential equations
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Wikidata QID: Q126421051
description: scientific article; zbMATH DE number 1787984