An asymptotic theorem for systems of linear differential equations.

Devinatz, Allen

doi:10.1090/S0002-9947-1971-0283312-0

An asymptotic theorem for systems of linear differential equations.
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by Allen Devinatz

Trans. Amer. Math. Soc. 160 (1971), 353-363

DOI: https://doi.org/10.1090/S0002-9947-1971-0283312-0

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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 \[ y’(t) = [A + V(t) + R(t)]y(t),\] 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

Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
Allen Devinatz, The deficiency index of a certain class of ordinary self-adjoint differential operators, Advances in Math. 8 (1972), 434–473. MR 298102, DOI 10.1016/0001-8708(72)90006-0
A. Devinatz, The deficiency index of ordinary self-adjoint differential operators, Pacific J. Math. 16 (1966), 243–257. MR 185219, DOI 10.2140/pjm.1966.16.243
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
Norman Levinson, The asymptotic nature of solutions of linear systems of differential equations, Duke Math. J. 15 (1948), 111–126. MR 24538