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A Two-Point Boundary Problem for Ordinary Self-Adjoint Differential Equations of Fourth Order

Published online by Cambridge University Press:  20 November 2018

H. M. Sternberg  and
R. L. Sternberg
H. M. Sternberg
Affiliation:
Chestnut Hill 67, Mass.
R. L. Sternberg
Affiliation:
Laboratory for Electronics, Inc., Boston 14, Mass.
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The purpose of this note is to establish Theorem A below for the two-point homogeneous vector boundary problem

where the Pi(x) are given real m × m symmetric matrix functions of x with P0(x) positive definite and Pi(x) of class C2−i on an infinite interval [a, ∞), and where by a solution of (1.1) — (1.2) for a ≤ x1 < x2 < ∞ we understand a real m-dimensional column vector u = u(x) of class C2 on [a, ∞) which is such that Pi(x)u(2−i) is of class C2−i on [a, ∞) and which satisfies (1.1) — (1.2) with the former a vector identity on [a, ∞).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 416 - 419
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Hille, Einar, Non-oscillation theorems, Trans. Amer. Math. Soc, 64 (1948), 234–252.Google Scholar
2. Kaufman, H. and Sternberg, R. L., A two-point boundary problem for ordinary self-adjoint differential equations of even order, Duke Math. J., 20 (1953), 527–531.Google Scholar
3. Sternberg, Robert L., Variational methods and non-oscillation theorems for systems of differential equations, Duke Math. J., 19 (1952), 311–322.Google Scholar
4. Wintner, Aurel, On the Laplace-Fourier transcendents occurring in mathematical physics, Amer. J. Math., 69 (1947), 87–98.Google Scholar