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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.19 no.3 Temuco dic. 2017

http://dx.doi.org/10.4067/S0719-06462017000300015 

Articles

Periodicity and stability in neutral nonlinear differential equations by Krasnoselskii’s fixed point theorem

Bouzid Mansouri1 

Abdelouaheb Ardjouni2 

Ahcene Djoudi3 

1Univ Annaba, Faculty of Sciences, Department of Mathematics, P.O. Box 12, Annaba 23000, Algeria. E-mail: mansouri.math@yahoo.fr

2Univ Souk Ahras, Faculty of Sciences and Technology, Department of Mathematics and Informatics, P.O. Box 1553, Souk Ahras, 41000, Algeria. E-mail: abd_ardjouni@yahoo.fr

3Univ Annaba, Faculty of Sciences, Department of Mathematics, Applied Mathematics Lab, P.O. Box 12, Annaba 23000, Algeria

Abstract

The nonlinear neutral functional differential equation with variable delay

=p(t)-a(t)u(t)-a(t)q(t)g(u(t-r(t)))-b(t)f(u(t))+b(t)q(t)f(u(t-r(t))).

is investigated. By using Krasnoselskii’s fixed point theorem we obtain the existence and the asymptotic stability of periodic solutions. Sufficient conditions are established for the existence and the stability of the above equation. Our results extend some results obtained in the work (19).

Keywords and Phrases: Fixed point; periodic solutions; stability; neutral differential equations

Resumen

La ecuación diferencial funcional no-lineal neutral con retardo variable

=p(t)-a(t)u(t)-a(t)q(t)g(u(t-r(t)))-b(t)f(u(t))+b(t)q(t)f(u(t-r(t))).

es investigada. Usando el teorema del punto fijo de Krasnoselskii obtenemos la existencia y la estabilidad asintótica de las soluciones periódicas. Se establecen condiciones suficientes para la existencia y la estabilidad de soluciones de la ecuación anterior. Nuestros resultados extienden algunos de los resultados obtenidos en (19).

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement.

The authors would like to thank the anonymous referee for his/her valuable comments and good advice.

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