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Periodic solutions for $$n$$-th order delay differential equations with damping terms. (English) Zbl 1249.34206
The author proves the existence of periodic solutions of the $$n$$-th order delay differential equations $x^{(n)}(t)=\sum _{i=1}^s b_i\,[x^{(i)}(t)]^{2k-1}+f(x(t-\tau (t)))+p(t),$ where $$k,n,s\in {\mathbb N}$$, $$s\leq n-1$$, $$k\geq 2$$, $$b_i\in {\mathbb R}$$, $$f$$ is continuous, $$p$$ is continuous and periodic. The method involves a continuation theorem of J. L. Mawhin.
##### MSC:
 34K13 Periodic solutions to functional-differential equations 47N20 Applications of operator theory to differential and integral equations
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