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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.17 no.1 Temuco  2015

http://dx.doi.org/10.4067/S0719-06462015000100001 

Instability to vector lienard equation with multiple delays

Cemil Tunc
Department of Mathematics, Faculty of Science Yüzüncü Yıl University 65080, Van, Turkey cemtunc@yahoo.com


ABSTRACT
By making use of a special Lyapunov-Krasovskii functional and applying Krasovskii’s properties, we prove instability of zero solution of a modified vector Lienard equation with multiple constant delays that includes Van der Pol, Rayleigh and Lienard equations, widely encountered in applications.


RESUMEN
Usando un funcional especial de Lyapunov-Krasovskii y aplicando propiedades de Krasovskii, probamos la inestabilidad de la solución nula de una ecuación de Liénard vectorial modificada con retardos constantes múltiples que incluyen a las ecuaciones de Van der Pol, Rayleigh y Liénard ampliamente encontradas en las aplicaciones.

Keywords and Phrases: Lienard, Lyapunov-Krasovskii functional, instability, delay.
2010 AMS Mathematics Subject Classification: 34K12, 34K20.


 

References

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[3] L. E. Elsgolts and S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Translated from the Russian by John L. Casti. Mathematics in Science and Engineering, Vol. 105. Academic Press [A Subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973.
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[5] N. N. Krasovskii, Stability of Motion. Applications of Lyapunov’s Second Method to Differential Systems and Equations with Delay, Stanford, Calif.: Stanford University Press 1963
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[6] C. Tunc, On the instability of solutions to a Linard type equation with multiple deviating arguments. Afr. Mat. 25 (2014), no. 4, 1013- 1021.
[7] C. Tunc, Instability of solutions of vector Linard equation with constant delay. Bull. Math. Soc. Sci. Math. Roumanie, (2012), (accepted).
[8] C. Tunc, Stability to vector Lienard equation with constant deviating argument. Nonlinear Dynam. 73(3), (2013), 1245- 1251.


Received: April 2014. Accepted: November 2014.

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