Stability conditions of second order integrodifferential equations with variable delay
type: Item
instance of: scholarly article
title: Stability conditions of second order integrodifferential equations with variable delay
zbMATH Open document ID: 1469.34098
DOI: 10.1155/2014/371639
author: Dingheng Pi
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We investigate integrodifferential functional differential equations \(\ddot{x} + f(t, x, \dot{x}) \dot{x} + \int_{t - r(t)}^t a(t, s) g(x(s)) d s = 0\) with variable delay. By using the fixed point theory, we obtain conditions which ensure that the zero solution of this equation is stable under an exponentially weighted metric. Then we establish necessary and sufficient conditions ensuring that the zero solution is asymptotically stable. We will give an example to apply our results.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 7022247
Wikidata QID: Q59036800
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/371639
OpenAlex ID: W2167310173
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description: scientific article; zbMATH DE number 7022247