We prove the existence of half-entire parabolic solutions, asymptotic to a prescribed central configuration, for the equation

$$\ddot{x}=\nabla U(x)+\nabla W(t,x),x\in {\mathbb{R}}^d,$$

where $d⩾2$, $U$ is a positive and positively homogeneous potential with homogeneity degree $-\alpha$ with $\alpha \in ]0,2[$, and $W$ is a (possibly time-dependent) lower order term, for $|x|\to +\infty$, with respect to $U$. The proof relies on a perturbative argument, after an appropriate formulation of the problem in a suitable functional space. Applications to several problems of Celestial Mechanics (including the $N$-centre problem, the $N$-body problem and the restricted $(N+H)$-body problem) are given.

中文翻译：

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天体力学中的抛物线轨道：一种功能分析方法

我们证明了方程的半全抛物线解的存在，渐近于规定的中心配置

$$\ddot{\times }=\nabla 你(\times )+\nabla 宽(吨,\times ),\times \in {\mathbb{电阻}}^d,$$

哪里 $d⩾2$, $你$ 是具有同质度的正和正同质势 $-\alpha$ 与 $\alpha \in ]0,2[$，和 $宽$ 是（可能与时间相关的）低阶项，对于 $|\times |\to +\infty$，关于 $你$. 在合适的函数空间中对问题进行适当的表述之后，证明依赖于微扰论证。天体力学若干问题的应用（包括$N$-中心问题 $N$-身体问题和限制 $(N+高)$-身体问题）给出。