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New results on periodic solutions for a kind of Rayleigh equation. (English) Zbl 1212.34124
Summary: The paper deals with the existence of periodic solutions for a class of non-autonomous time-delay Rayleigh equations. By means of a continuation theorem of the coincidence degree and a priori estimates, some new results on the existence of periodic solutions are established.
MSC:
 34C25 Periodic solutions of ODE 47N20 Applications of operator theory to differential and integral equations
References:
 [1] F. D. Chen: Existence and uniqueness of almost periodic solutions for forced Rayleigh equations. Ann. Differ. Equations 17 (2001), 1–9. [2] F. D. Chen, X. X. Chen, F. X. Lin, J. L. Shi: Periodic solution and global attractivity of a class of differential equations with delays. Acta Math. Appl. Sin. 28 (2005), 55–64. (In Chinese.) [3] K. Deimling: Nonlinear Functional Analysis. Springer, Berlin, 1985. [4] R. E. Gaines, J. L. Mawhin: Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics, Vol. 568. Springer, Berlin, 1977. [5] C. Huang, Y. He, L. Huang, W. Tan: New results on the periodic solutions for a kind of Reyleigh equation with two deviating arguments. Math. Comput. Modelling 46 (2007), 604–611. · Zbl 1161.34345 · doi:10.1016/j.mcm.2006.11.024 [6] F. Liu: On the existence of the periodic solutions of Rayleigh equation. Acta Math. Sin. 37 (1994), 639–644. (In Chinese.) [7] S. P. Lu, W. G. Ge: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Anal., Theory Methods Appl. 56 (2004), 501–514. · Zbl 1078.34048 · doi:10.1016/j.na.2003.09.021 [8] S. P. Lu, W. G. Ge, Z. X. Zheng: Periodic solutions for a kind of Rayleigh equation with a deviating argument. Appl. Math. Lett. 17 (2004), 443–449. · Zbl 1073.34081 · doi:10.1016/S0893-9659(04)90087-0 [9] S. P. Lu, W. G. Ge, Z. X. Zheng: Periodic solutions for a kind of Rayleigh equation with a deviating argument. Acta Math. Sin. 47 (2004), 299–304. [10] L. Peng: Periodic solutions for a kind of Rayleigh equation with two deviating arguments. J. Franklin Inst. 7 (2006), 676–687. · Zbl 1114.34051 · doi:10.1016/j.jfranklin.2006.04.001 [11] G.-Q. Wang, S. S. Cheng: A priori bounds for periodic solutions of a delay Rayleigh equation. Appl. Math. Lett. 12 (1999), 41–44. · Zbl 0980.34068 · doi:10.1016/S0893-9659(98)00169-4 [12] G.-Q. Wang, J. R. Yan: Existence theorem of periodic positive solutions for the Rayleigh equation of retarded type. Portugal. Math. 57 (2000), 153–160. [13] G.-Q. Wang, J. R. Yan: On existence of periodic solutions of the Rayleigh equation of retarded type. Int. J. Math. Math. Sci. 23 (2000), 65–68. · Zbl 0949.34059 · doi:10.1155/S0161171200001836 [14] Y. Zhou, X. Tang: On existence of periodic solutions of Rayleigh equation of retarded type. J. Comput. Appl. Math. 203 (2007), 1–5. · Zbl 1115.34067 · doi:10.1016/j.cam.2006.03.002