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Transactions of the American Mathematical Society

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An asymptotic theorem for systems of linear differential equations.


Author: Allen Devinatz
Journal: Trans. Amer. Math. Soc. 160 (1971), 353-363
MSC: Primary 34.50
DOI: https://doi.org/10.1090/S0002-9947-1971-0283312-0
MathSciNet review: 0283312
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Abstract | References | Similar Articles | Additional Information

Abstract: Asymptotic estimates are obtained for a complete linearly independent set of solutions of a linear system of differential equations of the form

$\displaystyle y'(t) = [A + V(t) + R(t)]y(t),$

where $ A$ is a constant $ n \times n$ matrix with $ n$ distinct eigenvalues, $ R(t)$ is an integrable matrix valued function on $ (0,\infty )$ and $ V(t)$ is an $ n \times n$ matrix valued function having certain differentiability properties. The theorem that is obtained generalizes a theorem of N. Levinson, Duke Math. J. 15 (1948), 111-126.

References [Enhancements On Off] (What's this?)

  • [1] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 16, 1022. MR 0069338 (16:1022b)
  • [2] A. Devinatz, The deficiency index of a certain class of ordinary self-adjoint differential operators, Advances in Math. (to appear). MR 0298102 (45:7154)
  • [3] -, The deficiency index of ordinary self-adjoint differential operators, Pacific J. Math. 16 (1966), 243-257. MR 32 #2688. MR 0185219 (32:2688)
  • [4] M. V. Fedorjuk, Asymptotic methods in the theory of one-dimensional singular differential operators, Trudy Moskov. Mat. Obšč. 15 (1966), 296-345 = Trans. Moscow Math. Soc. 1966, 333-386. MR 34 #7870. MR 0208060 (34:7870)
  • [5] N. Levinson, The asymptotic nature of solutions of linear systems of differential equations, Duke Math. J. 15 (1948), 111-126. MR 9, 509. MR 0024538 (9:509h)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0283312-0
Keywords: Asymptotic estimates for solutions of systems of ordinary linear differential equations
Article copyright: © Copyright 1971 American Mathematical Society

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