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2 results

  • Periodic Solutions of an Indefinite Singular Equation Arising from the Kepler Problem on the Sphere

  • Robert Hakl, Manuel Zamora
  • Journal:
    Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
    Published online by Cambridge University Press:
    20 November 2018, pp. 173-190
    Print publication:
    01 February 2018
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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.

  • PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

  • Part of
  • JIFENG CHU, ZIHENG ZHANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 82 / Issue 3 / December 2010
    Published online by Cambridge University Press:
    14 September 2010, pp. 437-445
    Print publication:
    December 2010
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  • In this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.