Topological Methods in Nonlinear Analysis

On existence of periodic solutions for Kepler type problems

Pablo Amster and Julián Haddad

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We prove existence and multiplicity of periodic motions for the forced $2$-body problem under conditions of topological character. In different cases, the lower bounds obtained for the number of solutions are related to the winding number of a curve in the plane and the homology of a space in $\mathbb R^3$.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 465-476.

Dates
First available in Project Euclid: 21 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1482289224

Digital Object Identifier
doi:10.12775/TMNA.2016.053

Mathematical Reviews number (MathSciNet)
MR3642768

Zentralblatt MATH identifier
1375.34065

Citation

Amster, Pablo; Haddad, Julián. On existence of periodic solutions for Kepler type problems. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 465--476. doi:10.12775/TMNA.2016.053. https://projecteuclid.org/euclid.tmna/1482289224


Export citation

References

  • R. Abraham, J.E. Marsden and T.S. Ratiu, Manifolds, Tensor Analysis and Applications, Applied Mathematical Sciences 75, Springer, 1989.
  • P. Amster, J. Haddad, R. Ortega and A. J. Ureña, Periodic motions in forced problems of Kepler type, Nonlinear Differential Equations Appl. 18 (2011), 649–657.
  • P. Amster and M. Maurette, Periodic solutions of systems with singularities of repulsive type, Adv. Nonlinear Stud. 11 (2011), 201–220.
  • A. Banyaga and D. Hurtubise, Lectures on Morse Homology, Kluwer Texts in the Mathematical Sciences. Vol. 29, Springer, 2004.
  • J. Cronin, Fixed Points and Topological Degree in Nonlinear Analysis, Math. Surveys No. 11, Amer. Math. Soc. Providence R.I., 1964.
  • J. Haddad and P. Amster, Critical point theory in knot complements, Differential Geom. Appl. 36 (2014), 56–65.
  • J. Hale, Ordinary Differential Equations, Krieger Publishing Company, 1969.
  • H. Hopf, Vektorfelder in $n$-dimensionalen Mannigfaltigkeiten, Math. Ann. 96 (1926/1927), 225–250.
  • P. Martinez-Amores, J. Mawhin, R. Ortega and M. Willem, Generic results for the existence of nondegenerate periodic solutions of some differential systems with periodic nonlinearities, J. Differential Equations 91 (1991), 138–148.
  • J. Mawhin, Topological degree methods in nonlinear boundary value problems, Regional Conf. Ser. Math. 40, Amer. Math. Soc., Providence, RI, 1979.
  • J. Mawhin, Periodic solutions in the goldensSixties: the birth of a Continuation Theorem, Ten Mathematical Essays on Approximation in Analysis and Topology (J. Ferrera, J. López-Gómez, F.R. Ruiz del Portal, eds.), Elsevier 2005, 199–214.
  • E.H. Spanier, Algebraic Topology, Springer, 1994.