共查询到20条相似文献,搜索用时 15 毫秒
1.
Some new results are given concerning the behavior of the oscillatory solutions of first or second order delay differential equations. These results establish that all oscillatory solutions x of a first or second order delay differential equation satisfy x(t)=O(v(t)) as t→∞, where v is a nonoscillatory solution of a corresponding first or second order linear delay differential equation. Some applications of the results obtained are also presented. 相似文献
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In this paper, oscillatory and asymptotic properties of solutions of nonlinear fourth order neutral dynamic equations of the form $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = 0(H)$ and $(r(t)(y(t) + p(t)y(\alpha _1 (t)))^{\Delta ^2 } )^{\Delta ^2 } + q(t)G(y(\alpha _2 (t))) - h(t)H(y(\alpha _3 (t))) = f(t),(NH)$ are studied on a time scale $\mathbb{T}$ under the assumption that $\int\limits_{t_0 }^\infty {\tfrac{t} {{r(t)}}\Delta t = \infty } $ and for various ranges of p(t). In addition, sufficient conditions are obtained for the existence of bounded positive solutions of the equation (NH) by using Krasnosel’skii’s fixed point theorem. 相似文献
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In this paper, sufficient conditions have been obtained for oscillation/nonoscillation of a class of homogeneous/nonhomogeneous linear difference equations of third order. 相似文献
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Baruch Cahlon Darrell Schmidt 《Journal of Mathematical Analysis and Applications》2007,334(2):859-875
In this paper we study the asymptotic stability of the zero solution of even order linear delay differential equations of the form
6.
Lynn Erbe Raziye Mert Allan Peterson Ağacık Zafer 《Czechoslovak Mathematical Journal》2013,63(1):265-279
One of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor’s Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is sufficient for oscillation of even order dynamic equations on time scales. The arguments are based on Taylor monomials on time scales. 相似文献
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Jurang Yan 《Applied Mathematics Letters》2011,24(8):1455-1460
In this paper, under weaker hypothesis, the global existence of oscillatory solutions is established for a forced second order nonlinear delay differential equation. The results of this paper generalize and improve some known results. 相似文献
9.
In this paper, sufficient conditions have been obtained for oscillation of all solutions of a class of nonlinear neutral delay
difference equations of the form
$
\Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0
$
\Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0
相似文献
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A class of sufficient conditions are obtained for the existence of a unique 2π-periodic solution of even order differential equations, employing an initial value problem. 相似文献
12.
Using the generalized Riccati technique and the averaging technique, new oscillation criteria for certain even order delay differential equation of the form
13.
Chenghui Zhang Ravi P. Agarwal Martin Bohner Tongxing Li 《Applied Mathematics Letters》2013,26(2):179-183
Some new oscillation results are presented that improve those reported in [C. Zhang, T. Li, B. Sun, and E. Thandapani, On the oscillation of higher-order half-linear delay differential equations, Appl. Math. Lett. 24 (2011) 1618–1621]. 相似文献
14.
一阶中立型时滞微分方程的振动性 总被引:1,自引:0,他引:1
李雪梅 《纯粹数学与应用数学》2000,16(1):75-79
分别获得了中立型时滞微分方程「x(t)+px(t-γ」’+q(t)x(t-σ)=0的振动性和非振动性的充分条件,其中p〉0,q(t)是一个正的周期函数。 相似文献
15.
Oleg Palumbíny 《Czechoslovak Mathematical Journal》1999,49(4):779-790
The paper deals with the oscillation of a differential equation L
4
y + P(t)L
2
y + Q(t)y 0 as well as with the structure of its fundamental system of solutions. 相似文献
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具有变系数的偶数阶中立型差分方程的振动性 总被引:1,自引:0,他引:1
杨莉 《纯粹数学与应用数学》2008,24(4)
考虑了一类具有变系数的偶数阶中立型差分方程的振动性,通过建立一个比较定理,获得一些一类具有变系数的偶数阶中立型差分方程的振动性的充分条件. 相似文献
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Alexander Weinstein 《Annali di Matematica Pura ed Applicata》1955,39(1):245-254
Summary The general solution for a class of equations of even order is expressed as a sum of solutions of equations of second order.
To Mauro Picone on his 70th birthday.
This research was supported in part by the United States Air Force under Contract No. AF(600)-573 — monitored by the Office of Scientific Research, Air Research and Development Command. 相似文献
20.
Said R. Grace Ravi P. Agarwal Sandra Pinelas 《Journal of Applied Mathematics and Computing》2011,35(1-2):525-536
We present some new necessary and sufficient conditions for the oscillation of second order nonlinear dynamic equation $$\bigl(a\bigl(x^{\Delta }\bigr)^{\alpha }\bigr)^{\Delta }(t)+q(t)x^{\beta }(t)=0$$ on an arbitrary time scale $\mathbb{T}$ , where α and β are ratios of positive odd integers, a and q are positive rd-continuous functions on $\mathbb{T}$ . Comparison results with the inequality $$\bigl(a\bigl(x^{\Delta }\bigr)^{\alpha }\bigr)^{\Delta }(t)+q(t)x^{\beta }(t)\leqslant 0\quad (\geqslant 0)$$ are established and application to neutral equations of the form $$\bigl(a(t)\bigl(\bigl[x(t)+p(t)x[\tau (t)]\bigr]^{\Delta }\bigr)^{\alpha }\bigr)^{\Delta }+q(t)x^{\beta }\bigl[g(t)\bigr]=0$$ are investigated. 相似文献
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