The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and the Euler formulation of elasticity theory for spherically symmetric bodies introduced recently by the authors. Examples of elastic materials covered by the results of this paper are Saint Venant-Kirchhoff, John and Hadamard materials.

中文翻译：

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静态自引力牛顿弹性球

在弹性材料的本构方程的一般假设下证明了静态自引力牛顿弹性球的存在。该证明使用了有限维动力系统理论和作者最近介绍的球对称体弹性理论的欧拉公式。本文结果涵盖的弹性材料示例包括 Saint Venant-Kirchhoff、John 和 Hadamard 材料。