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Periodic solutions to a forced Kepler problem in the plane
| Content Provider | Semantic Scholar |
|---|---|
| Author | Boscaggin, Alberto Dambrosio, Walter Papini, Duccio |
| Copyright Year | 2019 |
| Abstract | Given a smooth function $U(t,x)$, $T$-periodic in the first variable and satisfying $U(t,x) = \mathcal{O}(\vert x \vert^{\alpha})$ for some $\alpha \in (0,2)$ as $\vert x \vert \to \infty$, we prove that the forced Kepler problem $$ \ddot x = - \dfrac{x}{|x|^3} + \nabla_x U(t,x),\qquad x\in {\mathbb{R}}^2, $$ has a generalized $T$-periodic solution, according to the definition given in the paper [Boscaggin, Ortega, Zhao, \emph{Periodic solutions and regularization of a Kepler problem with time-dependent perturbation}, Trans. Amer. Math. Soc, 2018]. The proof relies on variational arguments. |
| Starting Page | 301 |
| Ending Page | 314 |
| Page Count | 14 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/proc/14719 |
| Volume Number | 148 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1902.08407v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/proc%2F14719 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
