Skip to main content
Log in

On Shifts along Trajectories

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

The extension of the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand sides based on the construction of a new version of the method of shifts along trajectories is continued.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. V. V. Filippov, “On the Aronszajn theorem,” Differentsial'nye Uravneniya [Differential Equations], 33 (1994), no. 1, 75-79.

    Google Scholar 

  2. V. V. Filippov, “On the existence of periodic solutions,” Mat. Zametki [Math. Notes], 61 (1997), no. 5, 769-784.

    Google Scholar 

  3. V. V. Filippov, “On the homological properties of solution sets of ordinary differential equations,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 188 (1997), no. 6, 139-160.

    Google Scholar 

  4. V. V. Filippov, “On the Dirichlet problem for a vector second-order ordinary differential equation,” Differentsial'nye Uravneniya [Differential Equations], 33 (1997), no. 8, 1057-1068.

    Google Scholar 

  5. V. V. Filippov, “The topological structure of spaces of solutions of ordinary differential equations,” Uspekhi Mat. Nauk [Russian Math. Surveys], 48 (1993), no. 1, 103-154.

    Google Scholar 

  6. V. V. Filippov, Spaces of Solutions of Ordinary Differential Equations [in Russian], Moskov. Gos. Univ., Moscow, 1993.

    Google Scholar 

  7. V. V. Filippov, “Basic topological structures of the theory of ordinary differential equations,” in: Topology in Nonlinear Analysis, vol. 35, Banach Center Publications, Warsaw, 1996, pp. 171-192.

    Google Scholar 

  8. V. V. Filippov, Basic Topological Structures of Ordinary Differential Equations, Kluwer Academic Publishers, Dordrecht-Boston-London, 1998.

    Google Scholar 

  9. V. V. Filippov, “A mixture of the Leray-Schauder and Poincare-Andronov methods in the problem about periodic solutions of ordinary differential equations,” Differentsial'nye Uravneniya [Differential Equations], 35 (1999), no. 12, 1709-1711.

    Google Scholar 

  10. V. V. Filippov, “Remarks on periodic solutions of ordinary differential equations,” J. Dynam. Control Systems, 6 (2000), no. 3, 431-451.

    Google Scholar 

  11. R. Engelking, General Topology, PWN, Warsaw, 1983.

    Google Scholar 

  12. V. V. Filippov, “Remarks on guiding functions and periodic solutions,” Differentsial'nye Uravneniya [Differential Equations] (to appear).

  13. J. Mawhin, “Continuation theorems and periodic solutions of ordinary differential equations,” in: Topological Methods in Differential Equations and Inclusions, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995, pp. 291-376.

    Google Scholar 

  14. A. M. Krasnosel'skii, M. A. Krasnosel'skii, and J. Mawhin, “On some conditions for existence of forced periodic oscillations,” Differential Integral Equations, 5 (1992), 1267-1273.

    Google Scholar 

  15. V. V. Filippov, “On the comparison theorem,” Mat. Zametki [Math. Notes], 57 (1995), no. 4, 606-624.

    Google Scholar 

  16. L. Vietoris, “Ñber den höheren Zusammenhang kompakter Räume und eine Klass von zusammen hangstreuen Abbildungen,” Math. Ann., 97 (1927), 454-472.

    Google Scholar 

  17. E. G. Begle, “The Vietoris mapping theorem for bicompact spaces,” Ann. of Math. (2), 51 (1950), no. 3, 534-543.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Filippov, V.V. On Shifts along Trajectories. Mathematical Notes 74, 266–277 (2003). https://doi.org/10.1023/A:1025064426702

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025064426702

Navigation