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Volume 18,     Number 4,     Winter 2010

 

ASYMPTOTIC STABILITY OF DELAY
DIFFERENTIAL EQUATIONS VIA FIXED
POINT THEORY AND APPLICATIONS
MENG FAN, ZHINAN XIA AND HUAIPING ZHU

Abstract. Nonlinear delay differential equations have been widely used to study the dynamics in biology, but the stability of such equations are challenging. In this paper, new criteria are established for the asymptotic stability of some nonlinear delay differential equations with finite delay via fixed point theory. The techniques involve both the contractive mapping principle and Schauder's fixed point theorem. The criteria are then applied to obtain the stability of some well known models in physiology and ecology.

 

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