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Periodic solutions of nth order delay Rayleigh equations

Gen-Qiang Wang, Sui Sun Cheng (2002)

Annales Polonici Mathematici

A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.

Periodic Solutions of Periodic Retarded Functional Differential Equations

Marcin Pawłowski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) x ' ( t ) = f ( t , x t ) , where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.

Permanence and global exponential stability of Nicholson-type delay systems

Zhonghuai Wu, Jianying Shao, Mingquan Yang, Wei Gao (2011)

Annales Polonici Mathematici

We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].

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