Skip to main content
SpringerLink
Log in

On dichotomies for solutions ofn-th order linear differential equations

  • Published:
Mathematische Annalen 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. Brinck, I.: Self-adjointness and spectra of Sturm-Liouville operators. Math. Scand.7, 219–239 (1959).

    Google Scholar 

  2. Ganelius, T.: Un théorème taubérien pour la transformation de Laplace. C. R. Acad. Sci. (Paris)242, 719–721 (1956).

    Google Scholar 

  3. Hartman, P., andA. Wintner: An oscillation theorem for continuous spectra. Proc. Nat. Acad. Sci. U. S.33, 276–379 (1947).

    Google Scholar 

  4. Hartman, P.: Differential equations with non-oscillatory eigenfunctions. Duke Math. J.15, 697–709 (1948).

    Google Scholar 

  5. Hartman, P.: On bounded Green's kernels for second order linear ordinary differential equations. Am. J. Math.73, 646–656 (1951).

    Google Scholar 

  6. Hartman, P.: On linear second order differential equations with small coefficients. Am. J. Math.73, 955–962 (1951).

    Google Scholar 

  7. Hartman, P.: On the essential spectra of symmetric operators in Hilbert space. Am. J. Math.75, 229–240 (1953).

    Google Scholar 

  8. Hartman, P.: On the ratio On the ratiof(t+cf −α(t))/f(t), Boll. U. M. I., (3)14, 57–61 (1959).

    Google Scholar 

  9. Massera, J. L., andJ. J. Schäffer: Linear differential equations and functional analysis. I. Ann. Math.67, 517–573 (1956).

    Google Scholar 

  10. Massera, J. L., andJ. J. Schäffer: Linear differential equations and functional analysis. IV. Math. Ann.139, 287–342 (1959).

    Google Scholar 

  11. Schäffer, J. J.: Function spaces with translations. Math. Ann.137, 209–262 (1959).

    Google Scholar 

  12. Schäffer, J. J.: Addendum: Function spaces with translation. Math. Ann.138, 141–144 (1959).

    Google Scholar 

  13. Schäffer, J. J.: Linear differential equations and functional analysis. V. Math. Ann.140, 308–321 (1960).

    Google Scholar 

  14. Schäffer, J. J.: Linear differential equations and functional analysis. VI. Math. Ann.,145, 354–400 (1962).

    Google Scholar 

  15. Weyl, H.: Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann.68, 222–269 (1910).

    Google Scholar 

  16. Wintner, A.: (L 2)-connections between the potential and kinetic energies of linear systems. Am. J. Math.69, 5–13 (1949).

    Google Scholar 

  17. Wintner, A.: On the non-existence of conjugate points. Am. J. Math.73, 368–380 (1951).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Baltimore

    Philip Hartman

Authors
  1. Philip Hartman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by the Air Force Office of Scientific Research.

Acknowledgement. The author wishes to acknowledge the help he has received with the work on and writing of this paper fromJ. J. Schäffer in numerous discussions and a lengthy correspondence. This paper was completely revised afterSchäffer made the manuscript of [14] available to the author.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hartman, P. On dichotomies for solutions ofn-th order linear differential equations. Math. Ann. 147, 378–421 (1962). https://doi.org/10.1007/BF01452423

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01452423

Keywords

Search

Navigation