A new generalization of the Sturm comparison theorem to selfadjoint systems

A new generalization of the Sturm comparison theorem to selfadjoint systems
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Proc. Amer. Math. Soc. 68 (1978), 185-188

DOI: https://doi.org/10.1090/S0002-9939-1978-0470327-4

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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

Shair Ahmad and A. C. Lazer, Component properties of second order linear systems, Bull. Amer. Math. Soc. 82 (1976), no. 2, 287–289. MR 399574, DOI 10.1090/S0002-9904-1976-14025-6
Shair Ahmad and Alan C. Lazer, On the components of extremal solutions of second order systems, SIAM J. Math. Anal. 8 (1977), no. 1, 16–23. MR 430409, DOI 10.1137/0508002
W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR 0460785
I. M. Gelfand and S. V. Fomin, Calculus of variations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. Revised English edition translated and edited by Richard A. Silverman. MR 0160139
Marston Morse, A generalization of the sturm separation and comparison theorems in $n$-space, Math. Ann. 103 (1930), no. 1, 52–69. MR 1512617, DOI 10.1007/BF01455690
William T. Reid, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0273082

Mémoire sur les équations différentielles linéaires de second ordre

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