相对论性Kepler问题的周期解：变分方法
Periodic solutions to relativistic Kepler problems: a variational approach
摘要：
我们研究平面上的相对论性开普勒问题。首先，利用非光滑临界点理论，证明了在一般的梯度型时间周期外力作用下，存在两个无限族的T-周期解，用它们绕奇点的卷绕数表示：第一个族是局部极小值序列，而第二个族则来自作用泛函的山路型几何.其次，我们利用Morse指标理论和作用泛函的水平估计，研究了非强迫问题的圆形和非圆形周期解的极小性。
英文摘要：
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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