Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A characterization of positive linear functionals and oscillation criteria for matrix differential equations

Author: Terry Walters
Journal: Proc. Amer. Math. Soc. 78 (1980), 198-202
MSC: Primary 34C10; Secondary 34G10
MathSciNet review: 550493
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Etgen and Pawlowski have recently given criteria for oscillation of matrix differential equations which involve the value of positive linear functionals on the matrices appearing in a matrix differential equation. We characterize these functionals and indicate relationships to eigenvalue criteria for oscillation. Our results are also useful for the detection of the oscillation of particular matrix differential equations.

References [Enhancements On Off] (What's this?)

  • [1] R. Bellman, Introduction to matrix analysis, McGraw-Hill, New York, 1960. MR 0122820 (23:A153)
  • [2] G. J. Etgen and J. F. Pawlowski, A comparison theorem and oscillation criteria for second order differential systems, Pacific J. Math. 72 (1977), 59-69. MR 0450675 (56:8968)
  • [3] A. G. Kartsatos, Oscillation of nonlinear systems of matrix differential equations, Proc. Amer. Math. Soc. 30 (1971), 97-101. MR 0280798 (43:6517)
  • [4] A. G. Kartsatos and T. J. Walters, Origins of oscillation criteria of operator differential equations in Hilbert space, J. Math. Anal. Appl. 67 (1979), 12-16. MR 524459 (80b:34074)
  • [5] K. Kreith, Oscillation theory, Lecture Notes in Math., vol. 324, Springer-Verlag, Berlin and New York, 1973.
  • [6] C. E. Rickart, Banach algebras, Van Nostrand, New York, 1960. MR 0115101 (22:5903)
  • [7] D. F. St. Mary, On transformation and oscillation of linear differential systems, Canad. J. Math. 19 (1977), 392-399. MR 0427744 (55:774)
  • [8] C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968. MR 0463570 (57:3515)
  • [9] E. C. Tomastik, Oscillation of nonlinear matrix differential equations of second order, Proc. Amer. Math. Soc. 19 (1968), 1427-1431. MR 0232046 (38:372)
  • [10] -, Oscillation of systems of second order differential equations, J. Differential Equations 9 (1971), 436-442. MR 0274863 (43:621)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10, 34G10

Retrieve articles in all journals with MSC: 34C10, 34G10

Additional Information

Keywords: Oscillation, matrix differential equations, positive linear functionals
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society