Abstract.
In this paper, we study the existence of periodic solutions of Rayleigh equation
where f, g are continuous functions and p is a continuous and 2π-periodic function. We prove that the given equation has at least one 2π-periodic solution provided that f(x) is sublinear and the time map of equation x′′ + g(x) = 0 satisfies some nonresonant conditions. We also prove that this equation has at least one 2π-periodic solution provided that g(x) satisfies \(\lim_{|x|\to+\infty}sgn(x)g(x) = +\infty\) and f(x) satisfies sgn(x)(f(x) − p(t)) ≥ c, for t ∈R, |x| ≥ d with c, d being positive constants.
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Received: July 1, 2002; revised: February 19, 2003
Research supported by the National Natural Science Foundation of China, No.10001025 and No.10471099, Natural Science Foundation of Beijing, No. 1022003 and by a postdoctoral Grant of University of Torino, Italy.
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Wang, Z. On the existence of periodic solutions of Rayleigh equations. Z. angew. Math. Phys. 56, 592–608 (2005). https://doi.org/10.1007/s00033-004-2061-z
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DOI: https://doi.org/10.1007/s00033-004-2061-z