Skip to main content
SpringerLink
Log in

An Existence Theorem for Periodic Solutions in Convex Sets with Applications

  • Published:
Results in Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. C. Alvarez — A.C. Lazer, An application of iopological degree to the periodic competing species problem, J. Austral. Math. Soc. (Ser.B), 28 (1986), 202–218.

    Article  MathSciNet  MATH  Google Scholar 

  2. H. Amann, A note on degree theory for gradient maps, Proc. Amer. Math. Soc, 85 (1982), 591–595.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Capietto, “Positive periodic solutions”, Magister Ph.Thesis, I.S.A.S., Trieste, 1988, in preparation.

  4. L. Cesari, Functional Analysis, nonlinear differential equations and the alternative method, in “Nonlinear Functional Analysis and Differential Equations”, (L. Cesari, R. Kannan and J.D. Schuur, eds), pp.1–197, Dekker, New York, 1977.

    Google Scholar 

  5. C. C. Conley, “Isolated invariant sets and the Morse index”, CBMS 38, Amer. Math. Soc, Providence R.I., 1978.

  6. E.N. Dancer, Multiple fixed points of positive mappings, J. für Reine und Angewandte Math., 371 (1986), 46–66.

    MathSciNet  MATH  Google Scholar 

  7. P. DE Mottoni — A. Schiaffino, Competition systems with periodic coefficients: a geometric approach, J. Math. Biol., 11 (1981), 319–335.

    Article  MathSciNet  MATH  Google Scholar 

  8. M.L.C. Fernandes — F. Zanolin, Repelling conditions for boundary sets using Liapunov-like functions.1: flow-invariance, terminal value problem and weak persistence, Rend. Sem. Mat. Univ. Padova, in print.

  9. M.L.C. Fernandes — F. Zanolin, On periodic solutions, in a given set, for differential systems, Trieste, 1987, preprint.

  10. M. Furi — M.P. Pera, Global branches of periodic solutions for forced differential equations on nonzero Euler characteristic manifolds, Boll. Un. Mat. Ital. 3-C(6) (1984), 157–170.

    MathSciNet  Google Scholar 

  11. M. Furi — M.P. Pera, A continuation principle for forced oscillations on differentiable manifolds, Pacific J.Math., 121 (1986), 321–338.

    Article  MathSciNet  MATH  Google Scholar 

  12. R.E. Gaines — J. Mawhin, “Coincidence degree and nonlinear differential equations”, Lecture Notes in Math., 586, Springer-Verlag, Berlin, 1977.

    Google Scholar 

  13. R.E. Gaines — J. Santanilla, A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations, Rocky Mountain J. Math., 12 (1982), 669–678.

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Granas, The Leray-Schauder index and the fixed point theory for arbitrary ANRs, Bull. Soc Math. France, 100 (1972), 209–228.

    MathSciNet  MATH  Google Scholar 

  15. G.B. Gustafson - K. Schmitt, A note on periodic solutions for delay differential systems, Proc Amer. Math. Soc, 42 (1974), 161–166.

    Article  MathSciNet  MATH  Google Scholar 

  16. H. Hofer, Variational and topological methods in partially ordered Hilbert spaces, Math. Ann., 261 (1981), 493–514.

    Article  MathSciNet  Google Scholar 

  17. M.A. Krasnosel’skii, “The operator of translation along the trajectories of differential equations”, Amer. Math. Soc., Providence R.I., 1968.

    Google Scholar 

  18. M.A. Krasnosel’skii — P.P. Zabreiko, “Geometrical methods of nonlinear Analysis”, Springer-Verlag, Berlin, 1984.

    Book  Google Scholar 

  19. J. Mawhin, Recent results on periodic solutions of differential equations, in “International Conference on Differential Equations”, (H. A. Antosiewicz, ed.), Proc. Conf. Southern California University, 1974, pp. 537–556, Academic Press, New York, 1975.

    Google Scholar 

  20. J. Mawhin, “Topological degree methods in nonlinear boundary value problems”, CBMS 40, Amer. Math. Soc., Providence R.I., 1979.

    Google Scholar 

  21. M. Nagumo, Über die Lage der Integralkurven gewöhnlicher Differentialgleichungen, Proc. Phys.-Math. Soc. Japan, (3) 24 (1942), 551–559.

    MathSciNet  MATH  Google Scholar 

  22. R.D. Nussbaum, “The fixed point index and some applications”, Les Presses de l’Université de Montréal, 1985.

  23. R. Reissig, Periodic solutions of a nonlinear n-th order vector differential equation, Ann. Mat. Pura Appl., (4) 87 (1970), 111–123.

    Article  MathSciNet  Google Scholar 

  24. K.P. Rybakowski, “The homotopy index and partial differential equations”, Springer-Verlag, Berlin, 1987.

    Book  MATH  Google Scholar 

  25. J. Santanilla, Some coincidence theorems in wedges, cones and convex sets, J. Math. Anal. Appl., 105 (1985), 357–371.

    Article  MathSciNet  MATH  Google Scholar 

  26. J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations, J. Math. Anal. Appl., 126 (1987), 397–408.

    Article  MathSciNet  MATH  Google Scholar 

  27. H.L. Smith, Periodic competitive differential equations and the discrete dynamics of competitive maps, J. Differential Equations, 64 (1986), 165–194.

    Article  MathSciNet  MATH  Google Scholar 

  28. H.L. Smith, Periodic solutions of periodic competitive and cooperative systems, SIAM J. Math. Anal., 17, (1986), 1289–1318.

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Srzednicki, On rest points of dynamical systems, Fund. Math., 126, (1985), 69–81.

    MathSciNet  MATH  Google Scholar 

  30. R. Srzednicki, Periodic and constant solutions via topological principle of Wazewski, Acta Math. Univ. lag., 26 (1987), 183–190.

    MathSciNet  Google Scholar 

  31. T. Wažewski, Sur un principe topologique de l’examen de l’allure asymptotique des intégrales des équations différentielles, Ann. Soc. Polon. Math., 20 (1947), 279–313.

    MathSciNet  Google Scholar 

  32. J.A. Yorke, Invariance for ordinary differential equations, Math. Systems Theory, I (1967), 353–372.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International School for Advanced Studies —, Str. Costiera, 11, 34014, Trieste —, Italy

    A. Capietto & F. Zanolin

Authors
  1. A. Capietto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Zanolin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Prof. Dr. R. Reissig on the occasion of his 65th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Capietto, A., Zanolin, F. An Existence Theorem for Periodic Solutions in Convex Sets with Applications. Results. Math. 14, 10–29 (1988). https://doi.org/10.1007/BF03323213

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323213

Keywords

Search

Navigation