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On the existence of periodic solutions to Rayleigh differential equation of neutral type in the critical case. (English) Zbl 1121.34072

Summary: The authors study the existence of periodic solutions for a second order neutral functional differential equation \[ (x(t)-cx(t-\tau))''=f(x'(t)) +g(t,x(t-\mu(t))) +e(t) \] in the critical case \(|c|=1\). By analyzing some properties of the linear difference operator \(A:[Ax](t)=x(t)-cx(t-\tau)\) and using Mawhin’s continuation theorem, some new results are obtained.

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
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References:

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