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



On the growth of solutions in the oscillatory case

Author: Robert M. Kauffman
Journal: Proc. Amer. Math. Soc. 51 (1975), 49-54
MSC: Primary 34C10
MathSciNet review: 0374559
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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 [Enhancements On Off] (What's this?)

  • [1] Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. MR 0061235
  • [2] W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR 0460785
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Keywords: Exponential growth, Fredholm operator, disconjugacy, essential spectrum
Article copyright: © Copyright 1975 American Mathematical Society

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