×

On a maximal number of period annuli. (English) Zbl 1210.34046

Summary: We consider the equation \(x''+g(x) = 0\), where \(g(x)\) is a polynomial, allowing the equation to have multiple period annuli. We detect the maximal number of possible period annuli for polynomials of odd degree and show how the respective optimal polynomials can be constructed.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] M. Sabatini, “Liénard limit cycles enclosing period annuli, or enclosed by period annuli,” The Rocky Mountain Journal of Mathematics, vol. 35, no. 1, pp. 253-266, 2005. · Zbl 1084.34037 · doi:10.1216/rmjm/1181069780
[2] S. Atslega and F. Sadyrbaev, “Period annuli and positive solutions of nonlinear boundary value problems,” in Proceedings of the 7th Congress of The International Society for Analysis, Its Applications and Computation (ISAAC ’09), July 2009, http://www.isaac2009.org/Congress/Welcome.html. · Zbl 1269.34028
[3] M. Sabatini, “On the period function of x\(^{\prime\prime}\)+f(x)x\(^{\prime}\)2+g(x)=0,” Journal of Differential Equations, vol. 196, no. 1, pp. 151-168, 2004. · Zbl 1048.34068 · doi:10.1016/S0022-0396(03)00067-6
[4] S. Atslega and F. Sadyrbaev, “Multiple solutions of the second order nonlinear Neumann BVP,” in Proceedings of the 6th International Conference on Differential Equations and Dynamical Systems, pp. 100-103, Watam Press, Baltimore, Md, USA, May 2009. · Zbl 1184.34048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.