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A new generalization of the Sturm comparison theorem to selfadjoint systems


Authors: Shair Ahmad and Alan C. Lazer
Journal: Proc. Amer. Math. Soc. 68 (1978), 185-188
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1978-0470327-4
MathSciNet review: 0470327
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Abstract: The Sturm Comparison Theorem is generalized to second order linear systems. It is based on a comparison of the elements of the matrices involved.


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

  • [1] S. Ahmad and A. C. Lazer, Component properties of second order linear systems, Bull. Amer. Math. Soc. 82 (1976), 287-289. MR 0399574 (53:3417)
  • [2] -, On the components of extremal solutions of second order systems, SIAM J. Math. Anal. 8 (1977), 16-23. MR 0430409 (55:3414)
  • [3] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin and New York, 1971. MR 0460785 (57:778)
  • [4] I. M. Gelfand and S. V. Fomin, Calculus of variations, Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 0160139 (28:3353)
  • [5] M. Morse, A generalization of the Sturm separation and comparison theorems in n-space, Math. Ann. 103 (1930), 72-90. MR 1512617
  • [6] W. T. Reid, Ordinary differential equations, Wiley, New York, 1971. MR 0273082 (42:7963)
  • [7] J. C. F. Sturm, Mémoire sur les équations différentielles linéaires de second ordre, J. Math. Pures Appl. 1 (1836), 106-186.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0470327-4
Keywords: Conjugate point, disconjugate, symmetric, selfadjoint, solution
Article copyright: © Copyright 1978 American Mathematical Society

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