非线性二阶中立型时滞微分方程的振动和非振动准则.pdf
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J. Sys. Sci. Math. Scis.
26(3) (2006, 6), 325–334
Æ
( 030008)
( 571158)
( 100080)
(E)
Æ
MR(2000) 34K11
1
[r (t)(x(t) + P (t)x(t − τ )) ] + Q (t)f (x(t − σ )) − Q (t)g (x(t − σ )) = 0 (E)
1 1 2 2
τ 0, σi ≥ 0, p(t) = 0, p, Qi ∈ C ([t0 , +∞), R), i = 1, 2., r ∈ C ([t0 , +∞), (0, +∞)),
f, g ∈ C (r, R) xf (x) 0, xg(x) 0, (x = 0).
[1,2]
Æ
Kulenovi´c [3] Æ
[3] (E). 2 Æ (E)
[3] [1] [4] 3 (E)
[5–8] (E)
(E)
2003-09-28, 2004-09-22.
326 26
1.1 (E) [Tx , +∞), Tx ≥ t0 x(t)
sup{|x(t)| : t ≥ T } 0, ∀T ≥ Tx
1.2 (E)
1.3 (E)
2
Æ (E)
(c ) f g Lipchitz Lipchitz L (A), L (A), A
1 f g
(c ) R(t) = t 1 ds, t ≥ t , Q (t) ≥ 0, +∞ R(t)Q (t)dt +∞, i = 1, 2.
2 t0 r (s) 0 i i
(c ) a 0, aQ (t) − Q (t) ≥ 0.
3 1 2
2.1 (c )–(c ) P
1 3 0
1
|P (t)| ≤ P
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