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 Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 5, Pages 1128–1142 (Mi izv2236)

On a comparison theorem for linear differential equations

T. A. Chanturiya

Abstract: It is proved in the paper that the equation $u^{(n)}=a(t)u$ has property $\mathrm B$ (i.e. each solution of it, in the case of even $n$, either is oscillating or satisfies the condition $|u^{(i)}(t)|\downarrow0$ for $t\to+\infty$ ($i=0,…, n-1$) or satisfies the condition $|u^{(i)}(t)|\uparrow+\infty$ for $t\to+\infty$ ($i=0,…,n-1$), and in the case of odd $n$, either is oscillating or satisfies the condition $|u^{(i)}(t)|\uparrow+\infty$ for $t\to+\infty$ ($i=0,…,n-1$)) if the equation $u^{(n)}=b(t)$ has the property $\mathrm B$ and $a(t)\geqslant b(t)\geqslant0$ for $t\in[0,+\infty)$.
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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:5, 1075–1088

Bibliographic databases:

UDC: 517.9
MSC: 34C10

Citation: T. A. Chanturiya, “On a comparison theorem for linear differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 40:5 (1976), 1128–1142; Math. USSR-Izv., 10:5 (1976), 1075–1088

Citation in format AMSBIB
\Bibitem{Cha76} \by T.~A.~Chanturiya \paper On a~comparison theorem for linear differential equations \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1976 \vol 40 \issue 5 \pages 1128--1142 \mathnet{http://mi.mathnet.ru/izv2236} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=432973} \zmath{https://zbmath.org/?q=an:0343.34023} \transl \jour Math. USSR-Izv. \yr 1976 \vol 10 \issue 5 \pages 1075--1088 \crossref{https://doi.org/10.1070/IM1976v010n05ABEH001826}