Skip to main content

On limit-point and Dirichlet-type results for second-order differential expressions

Part of the Lecture Notes in Mathematics book series (LNM,volume 564)

Keywords

  • Disjoint Interval
  • Deficiency Index
  • Weak Limit Point
  • Finite Singular Point
  • Ordinary Differential Expression

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F.V. Atkinson,: Limit-n criteria of integral type. Proc.Roy.Soc. Edinburgh (A), 73, 11, 1975, 167–198.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. F.V. Atkinson and W.D. Evans,: Solutions of a differential equation which are not of integrable square. Math.Z. 127 (1972), 323–332.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. L. Brinck,: Self-adjointness and spectra of Sturm-Liouville operators, Math.Scand. 7 (1959), 219–239.

    MathSciNet  MATH  Google Scholar 

  4. B.M. Brown and W.D. Evans,: On the limit-point and strong limit-point classification of 2nth order differential expressions with wildly oscillating coefficients. Math.Z. 134 (1973), 351–368.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M.S.P. Eastham,: On a limit-point method of Hartman. Bull. London Math. Soc. 4 (1972), 340–344.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. M.S.P.Eastham, W.D.Evans and J.B.McLeod,: The essential self-adjointness of Schrödinger-type operators, (to appear in Arch.Rat.Mech. and Analysis).

    Google Scholar 

  7. W.N. Everitt,: On the strong limit-point condition of second-order differential expressions. Proceedings of International Conference on Differential Equations (Los Angeles 1974). (Academic Press, New York, 1975) 287–307.

    MATH  Google Scholar 

  8. W.N. Everitt, M. Giertz and J.B. McLeod,: On the strong and weak limit-point classification of second-order differential expressions. Proc. London Math.Soc. (3) 29 (1974) 142–158.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. W.N. Everitt, M. Giertz and J. Weidmann,: Some remarks on a separation and limit-point criterion of second-order ordinary differential expressions. Math.Ann. 200, (1973), 335–346.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. P. Hartman,: The number of L2 solutions of x″+q(t)x=0. Amer.J.Math. 73, (1951) 635–645.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. R.S. Ismagilov,: Conditions for self-adjointness of differential equations of higher order. Soviet Math. 3, (1962) 279–283.

    MATH  Google Scholar 

  12. R.S. Ismagilov,: On the self-adjointtness of the Sturm-Liouville operator. Uspehi Mat. Nauk. 18, No.5 (113), (1963), 161–166.

    MathSciNet  MATH  Google Scholar 

  13. H. Kalf,: Remarks on some Dirichlet-type results for semi-bounded Sturm-Liouville operators. Math.Ann. 210, (1974), 197–205.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. I. Knowles,: Note on a limit-point criterion. Proc.Amer.Math.Soc. 41 (1973), 117–119.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. I. Knowles,: A limit-point criterion for a second-order linear differential operator. J.London Math.Soc. (2), 8 (1974), 719–727.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. N. Levinson,: Criteria for the limit-point case for second-order linear differential operators. Časopis pro pěsto ványi matematiky a fysiky. 74, (1949), 17–20.

    MathSciNet  MATH  Google Scholar 

  17. J.B. McLeod,: The limit-point classification of differential expressions. Spectral theory and asymptotics of differential equations (Mathematics Studies 13, North-Holland, Amsterdam, 1974), 57–67.

    Google Scholar 

  18. M.A. Naimark,: Linear differential operators. Part II (Ungar, New-York, 1968).

    MATH  Google Scholar 

  19. T.T.Read,: A limit point criterion for expressions with oscillating coefficients. (To appear).

    Google Scholar 

  20. W. N. Everitt,: A note on the Dirichlet condition for second-order differential expressions. Canadian J. Math. 28 (1976), 312–320.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Evans, W.D. (1976). On limit-point and Dirichlet-type results for second-order differential expressions. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087329

Download citation

  • DOI: https://doi.org/10.1007/BFb0087329

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08058-9

  • Online ISBN: 978-3-540-37517-3

  • eBook Packages: Springer Book Archive