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Zbl 1107.34037
Zhang, Meirong
Periodic solutions of equations of Emarkov-Pinney type.
(English)
[J] Adv. Nonlinear Stud. 6, No. 1, 57-67 (2006). ISSN 1536-1365

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 {\it P. Yan} and {\it M. Zhang} [Math. Methods Appl. Sci. 26, No. 12, 1067--1074 (2003; Zbl 1031.34040)] is removed.
MSC 2000:
*34C25 Periodic solutions of ODE

Keywords: singularity; periodic solution; nonresonance condition; degree; eigenvalue

Citations: Zbl 1031.34040

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