Periodic solutions of singular systems without the strong force condition. (English) Zbl 1129.37033

Franco, Daniel; Torres, Pedro J.

Proc. Am. Math. Soc. 136, No. 4, 1229-1236 (2008).

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:

37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C25	Periodic solutions to ordinary differential equations
34B16	Singular nonlinear boundary value problems for ordinary differential equations

Keywords:

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

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