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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 x ¨=f(t,x) with a strong singularity at the origin and semilinear growth at +. 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:
34C25Periodic solutions of ODE