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# Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere

Published:2017-02-21
Printed: Feb 2018
• Robert Hakl,
Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague, Czech Republic
• Manuel Zamora,
Departamento de Matemática, Grupo de Investigación en Sistemas Dinámicos y Aplicaciones, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile
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## Abstract

We study a second-order ordinary differential equation coming from the Kepler problem on $\mathbb{S}^2$. The forcing term under consideration is a piecewise constant with singular nonlinearity which changes sign. We establish necessary and sufficient conditions to the existence and multiplicity of $T$-periodic solutions.
 Keywords: singular differential equation, indefinite singularity, periodic solution, Kepler problem on $\mathbb{S}^1$, degree theory
 MSC Classifications: 34B16 - Singular nonlinear boundary value problems 34C25 - Periodic solutions 70F05 - Two-body problems 70F15 - Celestial mechanics

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