## 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
$x^{\prime\prime}(t)=-f(x(t-\tau)),\qquad x\in\mathbb R^n,\quad\tau>0$
with a particular symmetric behaviour of the vector-function $$f(x)$$ at $$x=0+$$ and $$x=+\infty$$. A lower estimate for the number of periodic solutions of period $$2\tau$$ 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:

 34K13 Periodic solutions to functional-differential equations

### Keywords:

differential delay equations; periodic solutions

Zbl 1095.34043
Full Text:

### References:

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