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Zbl 1129.37033
Franco, Daniel; Torres, Pedro J.
Periodic solutions of singular systems without the strong force condition. (English)
[J] Proc. Am. Math. Soc. 136, No. 4, 1229-1236 (2008). ISSN 0002-9939; ISSN 1088-6826/e

Summary: We present sufficient conditions for the existence of at least a non-collision periodic solution for singular systems under weak force conditions. We deal with two different types of systems. First, we assume that the system is generated by a potential, and then we consider systems without such hypothesis. In both cases we use the same technique based on Schauder fixed point theorem. Recent results in the literature are significantly improved.

MSC 2000:: *37J45 Periodic, homoclinic and heteroclinic orbits, etc.
34C25 Periodic solutions of ODE
34B16 Singular nonlinear boundary value problems

Keywords: non-collision periodic solution; singular systems under weak force conditions; Schauder fixed point theorem

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Zentralblatt MATH Berlin [Germany]