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Asymptotic properties of differential equations with involutions. (English) Zbl 1152.34384
Summary: 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.
MSC:
34K25Asymptotic theory of functional-differential equations
34K20Stability theory of functional-differential equations