Journal d’Analyse Mathématique

, Volume 36, Issue 1, pp 244–273 | Cite as

Disconjugacy of complex second-order matrix differential systems

  • Binyamin Schwarz
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. H. Barrett,Systems-disconjugacy of a fourth-order differential equation, Proc. Amer. Math. Soc.12 (1961), 205–213.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    P. R. Beesack,Nonoscillation and disconjugacy in the complex domain, Trans. Amer. Math. Soc.81 (1956), 211–242.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Friedland and Z. Nehari,Univalence conditions and Sturm-Liouville eigenvalues, Proc. Amer. Math. Soc.24 (1970), 595–603.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    F. R. Gantmacher,The Theory of Matrices, Vol. 1, Chelsea, New York, 1959.MATHGoogle Scholar
  5. 5.
    R. Hadass,On the zeros of the solutions of the differential equation y ((n)+p(z)y(z)=0, Pacific J. Math.31 (1969), 33–46.MATHMathSciNetGoogle Scholar
  6. 6.
    P. Hartman,Ordinary Differential Equations, Wiley, New York, 1964.MATHGoogle Scholar
  7. 7.
    P. Hartman and A. Wintner,On disconjugate differential systems, Canad. J. Math.8 (1956), 72–81.MathSciNetGoogle Scholar
  8. 8.
    E. Hille,Lectures on Ordinary Differential Equations, Addison-Wesley, Reading, Mass., 1969.MATHGoogle Scholar
  9. 9.
    W. J. Kim,The Schwarzian derivative and multivalence, Pacific J. Math.31 (1969), 717–724.MATHMathSciNetGoogle Scholar
  10. 10.
    P. Lancaster,Theory of Matrices, Academic Press, New York, 1969.MATHGoogle Scholar
  11. 11.
    M. Lavie,On disconjugacy and interpolation in the complex domain, J. Math. Anal. Appl.32 (1970), 246–263.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    D. London,On the zeros of the solutions of w″(z)+p(z)w(z)=0. Pacific J. Math.12 (1962), 979–991.MATHMathSciNetGoogle Scholar
  13. 13.
    Z. Nehari,The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc.55 (1949), 545–551.MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Z. Nehari,On the zeros of solutions of second-order linear differential equations, Amer. J. Math.76 (1954), 689–697.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Z. Nehari,Some criteria of univalence, Proc. Amer. Math. Soc.5 (1954), 700–704.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Z. Nehari,Univalent functions and linear differential equations, inLectures on Functions of a Complex Variable, University of Michigan Press, Ann Arbor, 1955, pp. 49–60.Google Scholar
  17. 17.
    Z. Nehari,On the zeros of solutions of n-th linear differential equations, J. London Math. Soc.,39 (1964), 327–232.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    V. V. Pokornyi,On some sufficient conditions for univalence, Dokl. Akad. Nauk. SSSR (N. S.)79 (1951), 743–746.MathSciNetGoogle Scholar
  19. 19.
    Chr. Pommerenke,Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.MATHGoogle Scholar
  20. 20.
    W. T. Reid,Ordinary Differential Equations, Wiley, New York, 1971.MATHGoogle Scholar
  21. 21.
    B. Schwarz,Norm conditions for disconjugacy of complex differential systems, J. Math. Anal. Appl.28 (1969), 553–568.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    B. Schwarz,Bounds for solutions of complex differential systems, J. Differential Equations16 (1974), 168–185.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    B. Schwarz,Injective differential systems, Illinois J. Math.22 (1978), 610–622.MATHMathSciNetGoogle Scholar
  24. 24.
    W. M. Whyburn,On self-adjoint ordinary differential equations of the fourth order, Amer. J. Math.52 (1930), 171–196.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1979

Authors and Affiliations

  • Binyamin Schwarz
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

Personalised recommendations