Periodic solutions to relativistic Kepler problems: a variational approach

2022/02/11 by Boscaggin, Alberto, Dambrosio, Walter, Papini, Duccio
#34C25 #58E05 #58E30 #70H40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.05604

Abstract

We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions, parameterized by their winding number around the singularity: the first family is a sequence of local minima, while the second one comes from a mountain pass-type geometry of the action functional. Secondly, we investigate the minimality of the circular and non-circular periodic solutions of the unforced problem, via Morse index theory and level estimates of the action functional.

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