Annali di Matematica Pura ed Applicata

, Volume 85, Issue 1, pp 83–91 | Cite as

Oscillation criteria for matrix differential equations with oscillatory coefficients

  • H. C. Howard


This paper considers the matrix differential equation Y″(x)+P(x)Y(x)=0 (and several generalizations) and establishes sufficient conditions for the existence of zeros of some of its solutions (in the sense that determinant Y(x)=0) when the coefficient P is « oscillatory ».


Differential Equation Oscillation Criterion Matrix Differential Equation Oscillatory Coefficient 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. H. Barrett,Fourth order boundary value problems and comparison theorems, Canad. J. Math., 13 (1961), pp. 625–638.MATHMathSciNetGoogle Scholar
  2. [2]
    G. J. Etgen,A note on trigonometric matrices, Proc. AMS, 17 (1966), pp. 1226–1232.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    —— ——,On the determinants of solutions of second-order matrix differential systems, J. Math Anal Appl. 18 (1967), pp. 587–598.CrossRefMathSciNetGoogle Scholar
  4. [4]
    R. W. Hunt,The behavior of solutions of ordinary self-adjoint differential equations of arbitrary even order, Pac. J. Math., 12 (1962), pp. 945–961.MATHGoogle Scholar
  5. [5]
    —— ——,Oscillation properties of even-order linear differential equations, Trans. AMS, 115 (1965), pp 54–61.CrossRefMATHGoogle Scholar
  6. [6]
    W. T. Reid,Oscillation criteria for self-adjoint differential systems, Trans AMS, 101 (1961), pp. 91–106.CrossRefMATHGoogle Scholar
  7. [7]
    J. S. W. Wong,Second order linear oscillations with integrable coefficients, Bull. AMS, 74 (1968), pp. 909–911.MATHGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • H. C. Howard
    • 1
  1. 1.USA

Personalised recommendations