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Asymptotic Behavior of Solutions of Differential Equations with Variable Delays

Authors:	Graef, John R. Qian, Chuanxi Zhang, Bo

Affiliation:	Department of Mathematics and Statistics, Mississippi State University Mississippi State, MS 39762, USA; graef{at}math.msstate.edu Department of Mathematics and Statistics, Mississippi State University Mississippi State, MS 39762, USA; qian{at}math.msstate.edu Department of Mathematics and Computer Science, Fayetteville State University Fayetteville, NC 28301, USA; bzhang{at}sbel.uncfsu.edu

Abstract:	The authors consider the system of forced differential equationswith variable delays whereB_j(t) is a continuous n x n matrix on R⁺, F $isin$ C(R⁺, Rⁿ) and ${tau}$ $isin$ C(R⁺, R⁺). Using Razumikhin-type techniques and Liapunov'sdirect method, they establish conditions to ensure the ultimateboundedness and the global attractivity of solutions of (),and when F(t) = 0, the asymptotic stability of the zero solution.Under those same conditions, they also show that is a necessary and sufficient condition for allof the above properties to hold. 1991 Mathematics Subject Classification*:34K15, 34C10.

Keywords:	forced equations systems variable delays boundedness global attractivity asymptotic stability
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