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Periodic solutions of equations of Emarkov-Pinney type. (English) Zbl 1107.34037

This paper provides a complete set of nonresonance conditions for the scalar differential equation \(\ddot x=f(t,x)\) with a strong singularity at the origin and semilinear growth at \(+\infty\). By combining the degree theory and a deep understanding of the relation between the Hill’s equation and the Ermakov-Pinney equation, a technical assumption required in the previous work of P. Yan and M. Zhang [Math. Methods Appl. Sci. 26, No. 12, 1067–1074 (2003; Zbl 1031.34040)] is removed.

MSC:

34C25 Periodic solutions to ordinary differential equations

Citations:

Zbl 1031.34040
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References:

[1] Tvrdy, Math Rach unkova Stanek and Singularities and Laplacians in boundary value problems for nonlinear ordinary differential equations in Handbook of Differential Equations Ordinary Differential Equations vol pp , to appear, Soc 112 pp 681– (1950)
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