Stability of linear differential equations with a distributed delay

Leonid Berezansky; Elena Braverman

doi:10.3934/cpaa.2011.10.1361

Article Contents

2011, Volume 10, Issue 5: 1361-1375. Doi: 10.3934/cpaa.2011.10.1361

This issue Previous Article Exterior differential systems and prolongations for three important nonlinear partial differential equations Next Article Duffing--van der Pol--type oscillator system and its first integrals

Stability of linear differential equations with a distributed delay

Leonid Berezansky^1, and
Elena Braverman^2,

1.
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105
2.
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4

Received: July 31, 2009

Revised: July 31, 2010

Published: August 2011

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Abstract

We present some new stability results for the scalar linear equation with a distributed delay

$\dot{x}(t) + \sum_{k=1}^m \int_{h_k(t)}^t x(s) d_s R_k(t,s) =0, h_k(t)\leq t,$ su$p_{t\geq 0}(t-h_k(t))<\infty,$

where the functions involved in the equation are not required to be continuous.
The results are applied to integro-differential equations, equations with several concentrated delays and equations of a mixed type.

Keywords:

Mathematics Subject Classification: Primary: 34K20; Secondary: 34K25.

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