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

  • 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 singular differential equation, indefinite singularity, periodic solution, Kepler problem on $\mathbb{S}^1$, degree theory
MSC Classifications: 34B16, 34C25, 70F05, 70F15 show english descriptions Singular nonlinear boundary value problems
Periodic solutions
Two-body problems
Celestial mechanics
34B16 - Singular nonlinear boundary value problems
34C25 - Periodic solutions
70F05 - Two-body problems
70F15 - Celestial mechanics
 

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