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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: 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.


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

  • [1] C. A. Swanson, Comparison and oscillation theory of linear differential equations, Mathematics in Science and Engineering, vol. 48, Academic Press, New York, 1968. MR 0463570 (57:3515)
  • [2] -, Comparison theorems for elliptic differential systems, Pacific J. Math. (to appear). MR 0262650 (41:7255)
  • [3] E. C. Tomastik, Oscillation of nonlinear matrix differential equations of second order, Proc. Amer. Math. Soc. 19(1968), 1427-1431. MR 38 #372. MR 0232046 (38:372)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0259248-2
Keywords: Nonlinear matrix differential inequality, oscillatory differential inequality, oscillation criterion, positive semidefinite matrix
Article copyright: © Copyright 1970 American Mathematical Society

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