Geodesic
Periodic Solutions of an Indefinite Singular Equation Arising from the Kepler Problemon the Sphere
Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 173-190

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DOI

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 that changes sign. We establish necessary and sufficient conditions to the existence and multiplicity of $T$ -periodic solutions.
DOI : 10.4153/CJM-2016-050-1
Mots-clés : 34B16, 34C25, 70F05, 70F15, singular differential equation, indefinite singularity, periodic solution, Kepler problem on S1, degree theory 
Hakl, Robert; Zamora, Manuel. Periodic Solutions of an Indefinite Singular Equation Arising from the Kepler Problemon the Sphere. Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 173-190. doi: 10.4153/CJM-2016-050-1
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     journal = {Canadian journal of mathematics},
     pages = {173--190},
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