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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 $$x^{\prime\prime}(t)=-f(x(t-\tau)),\qquad x\in\mathbb R^n,\quad\tau>0$$ 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 [{\it Z. M. Guo} and {\it J. S. Yu}, J. Differ. Equations 218, No. 1, 15--35 (2005; Zbl 1095.34043)].

34K13Periodic solutions of functional differential equations
Full Text: DOI
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