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Periodic solutions for a kind of Rayleigh equation with a deviating argument. (English) Zbl 1073.34081

The present paper is concerned with the existence of periodic solutions for the following Rayleigh delay equation \[ x''(t)+f(x'(t)) +g(x(t-\tau (t))) =p(t) \] by Mawhin’s coincidence degree theory. Sufficient conditions are given. An example is provided.

MSC:

34K13 Periodic solutions to functional-differential equations
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References:

[1] Huang, X.; Xiang, Z., On the existence of 2π-periodic solution for delay Duffing equation \(x\)″ \((t) + g(x(t\) −\(τ))) = p(t)\), Chinese Science Bulletin, 39, 3, 201-203 (1994), (in Chinese)
[2] Ma, S. W.; Wang, Z. C.; Yu, J. S., Coincidence degree and periodic solutions of Duffing equations, Nonlinear Analysis, TMA, 34, 443-460 (1998) · Zbl 0931.34048
[3] Lu, S.; Ge, W., On the existence of periodic solutions of second order differential equations with deviating arguments, Acta. Math. Sinica, 45, 4, 811-818 (2002), (in Chinese) · Zbl 1027.34079
[4] Lu, S.; Ge, W., Periodic solutions for a kind of second order differential equations with multiple deviating arguments, Applied Mathematics and Computation, 146, 195-209 (2003) · Zbl 1037.34065
[5] Wang, G.-Q, A priori bounds for periodic solutions of a delay Rayleigh equation, Appl. Math. Lett., 12, 3, 41-44 (1999) · Zbl 0980.34068
[6] Gaines, R. E.; Mawhin, J. L., (Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0339.47031
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