Abstract.This paper addresses the asymptotic behavior of a class of functional differential equations whose arguments transforms are involutions. Earlier work on asymptotic behavior involves only those involutions which have fixed points, and are consequently decreasing. In contrast we admit involutions without fixed points, allowing the possibility of non-decreasing. The monotonicity of the argument transform significantly influences the asymptotic behavior in some cases. Stability near equilibrium points is also studied.

Received: January 31, 2008

AMS Subject Classification: 34K05, 34K10, 34K15

Key Words and Phrases: differential equations, involutions, asymptotic behavior

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 4