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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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