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Existence of multiple periodic solutions for a class of second-order delay differential equations. (English) Zbl 1190.34083

The paper considers the second order multi-dimensional differential delay equation

x '' (t)=-f(x(t-τ)),x n ,τ>0

with a particular symmetric behaviour of the vector-function f(x) at x=0+ and x=+. A lower estimate for the number of periodic solutions of period 2τ in the system is given. The paper generalizes similar results derived for a like first order differential delay equation considered in [Z. M. Guo and J. S. Yu, J. Differ. Equations 218, No. 1, 15–35 (2005; Zbl 1095.34043)].

MSC:
34K13Periodic solutions of functional differential equations