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Existence of periodic solutions for $$n$$-th order differential equations with deviating argument. (English) Zbl 1185.34092
Summary: By employing the coincidence degree theory of Mawhin, we study the existence of periodic solutions for $$n$$-th order differential equations with deviating argument
$x^{(n)}+\sum^{n-1}_{i=2} b_ix^{(i)}(t)+f(x(t))x'(t)+g(t,x(t),x(t-\tau(t))) = p(t).$ Some new results on the existence of periodic solutions of the equations are obtained.

##### MSC:
 34K13 Periodic solutions to functional-differential equations 47N20 Applications of operator theory to differential and integral equations