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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the growth of solutions in the oscillatory case
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by Robert M. Kauffman PDF
Proc. Amer. Math. Soc. 51 (1975), 49-54 Request permission

Abstract:

Suppose that $A$ is a bounded continuously differentiable function from $[0,\infty )$ to the real $n \times n$ Hermitian matrices such that, for every $\varepsilon > 0$ and every $\lambda > 0$, there is an $a$ (depending on $\varepsilon$ and $\lambda$) such that ${D^2} - A - \varepsilon E$ and ${D^2} + A’/\lambda - \varepsilon E$ are disconjugate on $[a,\infty )$, where $E$ is the $n \times n$ identity matrix. It follows from the result of this paper that no solution of $({D^2} + A)f = 0$ can either grow or decay exponentially.
References
  • Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0061235
  • W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR 0460785
  • N. Dunford and J. T. Schwartz, Linear operators. II: Spectral theory. Self-adjoint operators in Hilbert space, Wiley, New York, 1963. MR 32 #6181.
  • Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 49-54
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374559-2
  • MathSciNet review: 0374559