论文标题
相对论开普勒问题的定期解决方案：一种变异方法
Periodic solutions to relativistic Kepler problems: a variational approach
论文作者
论文摘要
我们研究了平面中的相对论开普勒问题。首先，使用非平滑临界点理论，我们表明，在梯度类型的一般时间周期外部力下，有两个无限的T-周期性溶液家族，由它们周围的缠绕数量进行参数：第一个家族是局部最小值的序列，而第二个家庭来自山区通行的几何形状的动作功能。其次，我们通过莫尔斯指数理论和动作功能的水平估计值研究了未强制性问题的圆形和非圆周期解决方案的最小值。
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.
