On equations with delay depending on solution
type: Item
instance of: scholarly article
title: On equations with delay depending on solution
zbMATH Open document ID: 1012.34066
DOI: 10.1016/S0362-546X(01)00132-8
author: Michael Drakhlin
author: Elena Litsyn
author: A. Domoshnitsky
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-06-10T00:00:00Z
review text: The authors study the equation \(\dot x(t) +\sum_{i=1}^m A_i(t) x(t-(H_ix)(t))=f(t)\) in \(\mathbb{R}^n\) where \(A_i\) and \(f\) are measurable and essentially bounded functions and the \(H_i\) are scalar-valued measurable functions. The presence of the state-dependent time lag \(H_ix\) makes the equation nonlinear. Investigating the corresponding linear equations, sufficient conditions are obtained for the boundedness, oscillation and nonoscillation of the solutions.
reviewed by: Tibor Krisztin
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 1751627
zbMATH Keywords: functional-differential equations
zbMATH Keywords: state dependent delay
zbMATH Keywords: absorption method
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1751627