Positive cones and focal points for a class of 𝑛th-order differential equations

Keener, M. S.; Travis, C. C.

doi:10.1090/S0002-9947-1978-0479377-X

Positive cones and focal points for a class of $n$th-order differential equations
HTML articles powered by AMS MathViewer

by M. S. Keener and C. C. Travis

Trans. Amer. Math. Soc. 237 (1978), 331-351

DOI: https://doi.org/10.1090/S0002-9947-1978-0479377-X

PDF | Request permission

Abstract:

Necessary and sufficient conditions are obtained for both the existence and absence of focal points for a class of nth order linear differential equations. The techniques utilized the theory of ${\mu _0}$-positive operators with respect to a cone in a Banach space.

References

R. D. Gentry and C. C. Travis, Comparison of eigenvalues associated with linear differential equations of arbitrary order, Trans. Amer. Math. Soc. 223 (1976), 167–179. MR 425241, DOI 10.1090/S0002-9947-1976-0425241-X
R. D. Gentry and C. C. Travis, Existence and comparison of eigenvalues of $n$th order linear differential equations, Bull. Amer. Math. Soc. 82 (1976), no. 2, 350–352. MR 422747, DOI 10.1090/S0002-9904-1976-14062-1
Einar Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252. MR 27925, DOI 10.1090/S0002-9947-1948-0027925-7
M. A. Krasnosel′skiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964. Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron. MR 0181881
Zeev Nehari, Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500–516. MR 219781, DOI 10.1090/S0002-9947-1967-0219781-0

Green’s functions and disconjugacy

Curtis C. Travis, Comparison of eigenvalues for linear differential equations of order $2n$, Trans. Amer. Math. Soc. 177 (1973), 363–374. MR 316808, DOI 10.1090/S0002-9947-1973-0316808-5