Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with variable delay

 

Abdelouaheb Ardjouni, Ahcene Djoudi
University of Annaba, Algeria

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ABSTRACT

In this article we study the existence of positive periodic solutions for two types of second-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnosel-skii's fixedpoint theoremdealing withasum of twomappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Cheung, Ren and Han 7.

Subjclass : [2000 ] Primary 34K13, 34A34; Secondary 34K30, 34L30.

Keywords : Positive periodic solutions, nonlinear neutral differential equations, fixed point theorem.

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A. Ardjouni
Department of Mathematics,
Faculty of Sciences
University of Annaba,
P. O. Box 12 Annaba,
Algeria
e-mail : abd_ardjouni@yahoo.fr

 

A. Djoudi
Department of Mathematics,
Faculty of Sciences
University of Annaba,
P. O. Box 12 Annaba,
Algeria
e-mail : adjoudi@yahoo.com

Received : January 2013. Accepted : September 2013.