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Periodic Solutions of an Indefinite Singular Equation Arising from the Kepler Problemon the Sphere

Published online by Cambridge University Press:  20 November 2018

Robert Hakl  and
Manuel Zamora
Robert Hakl
Affiliation:
Institute of Mathematics, AS CR, Czech Republic e-mail: hakl@ipm.cz
Manuel Zamora
Affiliation:
Departamento de Matemática, Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile e-mail: mzamora@ubiobio.cl
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Abstract

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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.

Keywords

34B1634C2570F0570F15singular differential equationindefinite singularityperiodic solutionKepler problem on 𝕊1degree theory
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 1 , 01 February 2018 , pp. 173 - 190
Copyright
Copyright © Canadian Mathematical Society 2018

References

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