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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[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.