Oscillation criteria for second order self-adjoint matrix differential equations

N. Parhi; P. Praharaj

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 1, page 1-14
  • ISSN: 0066-2216

Abstract

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Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.

How to cite

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Parhi, N., and Praharaj, P.. "Oscillation criteria for second order self-adjoint matrix differential equations." Annales Polonici Mathematici 72.1 (1999): 1-14. <http://eudml.org/doc/262798>.

@article{Parhi1999,
abstract = {Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.},
author = {Parhi, N., Praharaj, P.},
journal = {Annales Polonici Mathematici},
keywords = {matrix differential equations; self-adjoint; oscillation; selfadjoint},
language = {eng},
number = {1},
pages = {1-14},
title = {Oscillation criteria for second order self-adjoint matrix differential equations},
url = {http://eudml.org/doc/262798},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Parhi, N.
AU - Praharaj, P.
TI - Oscillation criteria for second order self-adjoint matrix differential equations
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 1
SP - 1
EP - 14
AB - Some results concerning oscillation of second order self-adjoint matrix differential equations are obtained. These may be regarded as a generalization of results for the corresponding scalar equations.
LA - eng
KW - matrix differential equations; self-adjoint; oscillation; selfadjoint
UR - http://eudml.org/doc/262798
ER -

References

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  1. [1] J. H. Barrett, Oscillation theory of ordinary linear differential equations, Adv. Math. 3 (1969), 415-509, and Lectures on Differential Equations, R. McKelvey (ed.), Academic Press, New York, 1970. Zbl0213.10801
  2. [2] G. J. Butler and L. H. Erbe, Oscillation results for second order differential systems, SIAM J. Math. Anal. 17 (1986), 19-29. Zbl0583.34027
  3. [3] G. J. Butler, L. H. Erbe and A. B. Mingareli, Riccati techniques and variational principles in oscillation theory for linear systems, Trans. Amer. Math. Soc. 503 (1987), 263-282. 
  4. [4] W. J. Coles, An oscillation criterion for second order linear differential equations, Proc. Amer. Math. Soc. 19 (1968), 755-759. Zbl0172.11702
  5. [5] P. Hartman, On nonoscillatory linear differential equations of second order, Amer. J. Math. 74 (1952), 389-400. Zbl0048.06602
  6. [6] H. C. Howard, Oscillation criteria for matrix differential equations, Canad. J. Math. 19 (1967), 184-199. Zbl0148.07203
  7. [7] W. Leighton, On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37-47. Zbl0048.06503
  8. [8] A. B. Mingareli, On a conjecture for oscillation of second order ordinary differential systems, Proc. Amer. Math. Soc. 82 (1981), 593-598. 
  9. [9] E. S. Noussair and C. A. Swanson, Oscillation criteria for differential systems, J. Math. Anal. Appl. 36 (1971), 575-580. Zbl0222.34008
  10. [10] C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York, 1968. 
  11. [11] D. Willet, Classification of second order linear differential equations with respect to oscillation, Adv. Math. 3 (1969), 594-623, and Lectures on Differential Equations, R. McKelvey (ed.), Academic Press, New York, 1970. 
  12. [12] A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115-117. Zbl0032.34801
  13. [13] J. S. W. Wong, Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients, Trans. Amer. Math. Soc. 144 (1969), 197-215. Zbl0195.37402

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