Abstract and Applied Analysis

Stability Conditions of Second Order Integrodifferential Equations with Variable Delay

Dingheng Pi

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Abstract

We investigate integrodifferential functional differential equations x ̈ + f ( t , x , x ̇ ) x ̇ + 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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 371639, 11 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425048245

Digital Object Identifier
doi:10.1155/2014/371639

Mathematical Reviews number (MathSciNet)
MR3208532

Zentralblatt MATH identifier
07022247

Citation

Pi, Dingheng. Stability Conditions of Second Order Integrodifferential Equations with Variable Delay. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 371639, 11 pages. doi:10.1155/2014/371639. https://projecteuclid.org/euclid.aaa/1425048245


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