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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
MathSciNet review: 0283312
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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] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • [2] Allen Devinatz, The deficiency index of a certain class of ordinary self-adjoint differential operators, Advances in Math. 8 (1972), 434–473. MR 0298102
  • [3] A. Devinatz, The deficiency index of ordinary self-adjoint differential operators, Pacific J. Math. 16 (1966), 243–257. MR 0185219
  • [4] M. V. Fedorjuk, Asymptotic methods in the theory of one-dimensional singular differential operators, Trudy Moskov. Mat. Obšč. 15 (1966), 296–345 (Russian). MR 0208060
  • [5] Norman Levinson, The asymptotic nature of solutions of linear systems of differential equations, Duke Math. J. 15 (1948), 111–126. MR 0024538

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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