Oscillatory criteria for nonlinear matrix differential inequalities.
Author:
C. A. Swanson
Journal:
Proc. Amer. Math. Soc. 24 (1970), 824-827
MSC:
Primary 34.42
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259248-2
MathSciNet review:
0259248
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Abstract | References | Similar Articles | Additional Information
Abstract: Oscillation criteria are established for nonlinear matrix differential equations of the form $[A(x)V’]’ + B(x,\;V,\;V’)V = 0$ and associated differential inequalities. The hypothesis used recently by E. C. Tomastik, that $A$ and $B$ are positive definite, is weakened to the following: $A$ is positive semidefinite.
- C. A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York-London, 1968. Mathematics in Science and Engineering, Vol. 48. MR 0463570
- C. A. Swanson, Comparison theorems for elliptic differential systems, Pacific J. Math. 33 (1970), 445–450. MR 262650
- E. C. Tomastik, Oscillation of nonlinear matrix differential equations of second order, Proc. Amer. Math. Soc. 19 (1968), 1427–1431. MR 232046, DOI https://doi.org/10.1090/S0002-9939-1968-0232046-2
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Additional Information
Keywords:
Nonlinear matrix differential inequality,
oscillatory differential inequality,
oscillation criterion,
positive semidefinite matrix
Article copyright:
© Copyright 1970
American Mathematical Society