SCIENTIFIC ABSTRACT LEVIN, A.YU. - LEVIN, B.I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000929520004-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

2 1 "! 9
8/020/61/14i/oo6/ool/021
The stability of solutions of second ... CIII/C333
q(t) is of constant sign also necessary that
t
00 t
dt. q(s) lexp p (-C ) dT) ) do - co (12)
is satisfied.
Assume that the coefficients of (7) satisfy the conditions
0 - 0 . (10)
Let x(t) be an oscillating solution of (7). Let t n and t n+1 be
neighboring maximum points of the absolute value. Then
Cos I < 2
ch ys e7 (' +
Cos 71 t# v& th -Y, I > 2
Card 4/7

32419
3/020/61/14!/006/001/021
The stability of solutions of second ... C111/C333
Here it holdst 1/2 FM-- cos Y, - Y
(0 -e- -15 1/2 4m - coo Y2 (01' 12'- 2
for 1 4 2 Vm ; 1/2 rm a oh ~2 for 1>24-m
Let %P (1, m, M) - 0 for 1 >,- Am ; tp (1, m, M) - (P (1, m, M) for
1 < 2 JI .
Theorem 4: Assume that the coefficients of (7) satisfy the conditions
(10), where
Y (1, M, M) (14)
Then all solutions of (7) together with their derivatives are bounded
on (to, OD),.
Theorem 5: Assume that the coefficients of (7) satisfy the conditions
(10) and
OD t
t
dt exp p dr ds - co
Card 5/1~

1124i'31
S102 61/141/006/001/021
The stability of solutions of second - C!11YC333
where
kf (1, M, M) _:c 1 (15)
Then all solutions of (7) together with their derivatives tend to zero
for t ---)oo.
Let h be the root of the equation 1n h 4-0-1 - 2 arc sin 71- -
0 2 r
Theorem 6s Let the coefficients of (7) satisfy the conditions
0 1--- q ( t ) .6, MpQ 0,
where 2
M 0 for t> 0, F xij(t)> 0 for t> 0. A sequence of
functions xi(t) satisfies the inequalities x i(t)< m&xtx,(t,)Ix,(t2)1 for
11ird 1/2

S/208/62/002/005/007/009
Stabilization of solutions to ... B112/BI02
t1< t