## 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

Zbl 1031.34040
Full Text:

### 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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