Geodesic
Partially Bounded Solutions of Linear Ordinary Differential Equations
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 366-371

Voir la notice de l'article provenant de la source Cambridge University Press

Let R, R+, and R- be the intervals (-∞, ∞), [0, ∞), and ( — ∞, 0] respectively. Let m be a positive integer, and let be the algebra of all m X m matrices. Let A be a locally integrable function from R to We propose to study the problems(NH) u‘(t) = f(t) + A{t)u{t)and(H) v‘(t) =A(t)v(t)in Rm. (H) and (NH) will denote whole-line problems, whereas (H)+, (NH)+, (H)-, and (NH)- will denote corresponding semi-axis problems.In [1] (see also [2, Theorem 1, p. 131]), W. A. Coppel obtained necessary and sufficient conditions for each bounded Continuous/ on R+ to yield at least one bounded solution u of (NH)+. The present author [3] has determined that an analogous result holds for (NH). 
Lovelady, David Lowell. Partially Bounded Solutions of Linear Ordinary Differential Equations. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 366-371. doi: 10.4153/CJM-1975-044-1
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[1] 1. Coppel, W. A., On the stability of ordinary differential equations, J. London Math. Soc. 38 (1963), 255–260. Google Scholar

[2] 2. Coppel, W. A., Stability and asymptotic behavior of differential equations (D. C. Heath & Co., Boston, 1965). Google Scholar

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[6] 6. Schechter, M., Principles of functional analysis (Academic Press, New York, 1971). Google Scholar

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