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Coincidence degree and periodic solutions of Duffing equations. (English) Zbl 0931.34048
The authors consider the following Duffing equation with delay argument: $\ddot x(t)+ m^2\dot x+ g(x(t- \tau))= p(t),$ where $$\tau$$ is a nonnegative constant, $$m$$ is a positive integer, $$g(x)$$ is bounded and $$p(t)$$ is $$2\pi$$-periodic in $$t$$. Sufficient conditions which ensure solvability of the periodic problem are given. The approach uses a combination of Brouwer degree theory with a continuation theorem based on Mawhin’s coincidence degree. The particular example with $$g(x)= \sin x$$ is discussed.
Reviewer: P.Smith (Keele)

##### MSC:
 34K13 Periodic solutions to functional-differential equations 34C25 Periodic solutions to ordinary differential equations
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##### References:
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