Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-15T16:20:14.159Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation Criteria for Matrix Differential Inequalities(1)

Published online by Cambridge University Press:  20 November 2018

W. Allegretto  and
L. Erbe
W. Allegretto
Affiliation:
University of Alberta, Edmonton Alberta
L. Erbe
Affiliation:
University of Alberta, Edmonton Alberta
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Several authors have recently considered the problem of obtaining sufficient conditions for the oscillation of the quasilinear matrix differential equation

(1)

and the associated inequality VTLV ≤ 0 (as a form). Here A, B, and V are m x m matrix functions, A(x) is symmetric, positive semidefinite and continuous in an interval [a, ∞) and B(x,V, V') is symmetric and continuous in a≤ x < ∞ for all V and V'.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 5 - 10
Copyright
Copyright © Canadian Mathematical Society 1973

Footnotes

(1)

This research was supported, in part by National Research Council Grants A-7673 and A-8014.

References

1. Allegretto, W. and Swanson, C. A., Oscillation criteria for elliptic systems, Proc. Amer. Math. Soc. 27 (1971), 325–330.Google Scholar
2. Kreith, K., Oscillation criteria for nonlinear matrix differential equations, Proc. Amer. Math. Soc. 26 (1970), 270–272.Google Scholar
3. Leighton, W., On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37–47.Google Scholar
4. Marcus, M. and Mine, H., A survey of matrix theory and matrix inequalities Allyn and Bacon, Boston, Mass., 1964.Google Scholar
5. Noussair, E. and Swanson, C. A., Oscillation criteria for differential systems (to appear).Google Scholar
6. Swanson, C. A., Oscillation criteria for nonlinear matrix differential inequalities, Proc. Amer. Math. Soc. 24(1970), 824–827.Google Scholar
7. Tomastik, E. C., Oscillation of nonlinear matrix differential equations of second order, Proc. Amer. Math. Soc. 19 (1968), 1427–1431.Google Scholar
8. Tomastik, E. C., Oscillation of systems of second order differential equations, J. Differential Equations. 9 (1971), 436–442.Google Scholar