共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we deal with oscillatory and asymptotic properties of solutions of a fourth order sub-linear differential equation with the oscillatory operator. We establish conditions for the nonexistence of positive and bounded solutions and an oscillation criterion. 相似文献
2.
OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY 总被引:1,自引:0,他引:1
冯月才 《Annals of Differential Equations》2004,20(1):37-40
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation. 相似文献
3.
Oscillatory and Asymptotic Behavior of Solutions for Nonlinear Impulsive Delay Differential Equations 总被引:1,自引:0,他引:1
Wei-hua Mao An-hua Wan 《应用数学学报(英文版)》2006,22(3):387-396
The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established, Three illustrative examples are proposed to demonstrate the effectiveness of the conditions. 相似文献
4.
We show by a series of counterexamples that a commonly used assumption in the study of asymptotic and oscillatory properties of solutions to neutral differential equations is not valid. Appearing consequences and related open problems are briefly discussed. 相似文献
5.
Pavel Nesterov 《Monatshefte für Mathematik》2013,171(2):217-240
We use the method of averaging and the extension of the Levinson fundamental theorem to study the problem of asymptotic integration of a class of linear functional differential systems that contain oscillatory decreasing coefficients. Moreover, we construct the asymptotics for solutions of the second order delay differential equation that is close, in some sense, to harmonic oscillator. 相似文献
6.
We construct the asymptotic formulas for solutions of a certain linear second-order delay differential equation as independent variable tends to infinity. When the delay equals zero this equation turns into the so-called one-dimensional Schrödinger equation at energy zero with Wigner–von Neumann type potential. The question of interest is how the behaviour of solutions changes qualitatively and quantitatively when the delay is introduced in this dynamical model. We apply the method of asymptotic integration that is based on the ideas of the centre manifold theory in its presentation with respect to the systems of functional differential equations with oscillatory decreasing coefficients. 相似文献
7.
1IntroductionTheexistence,uniqueness,oscillatoryandasymptoticbehaviorofsolutionsofthefirstorderdifferentialequationswithpiecewiseconstantdelayhavebeenstudiedin[1-4].Butoscillatoryandasymptoticbehavioroffirstorderneutraldifferentialequationwithpiecewiseconstantdelayseemtoberarelyconsidered[5,6].Inthispaper,weconsidertheoscillatoryandasymptoticbehavioroffirstordernonlinearneutraldifferentialequationwithpiecewiseconstantdeviatingargumentsoftheformwherecisaconstant,p(t)EC[0, co),fEC(R,R)andxf(x)… 相似文献
8.
Asymptotic behavior of solutions for a nonlinear differential equation with constant impulsive jumps
We investigate the asymptotic behavior of solutions to the nonlinear neutral delay differential equation (1.1) with constant impulsive jumps and forced term. By employing a new approach which is different from Lyapunov functionals and an effective technic for the constant impulsive jumps, new sufficient conditions are obtained to guarantee every non-oscillatory/oscillatory solution of the equation tends to zero as t????. Our results improve and generalize some known results in the literature. 相似文献
9.
解决了一类带阻尼项的三阶脉冲微分方程的非振动解与其一阶、二阶导数的符号关系,用迭代法得到其振动性与渐近性的判别准则,并举例说明准则的有效性. 相似文献
10.
M. Bartušek M. Cecchi M. Marini 《Journal of Mathematical Analysis and Applications》2006,320(1):108-120
Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zero-counting function. 相似文献
11.
一阶变系数滞后型微分方程解的振动性积分条件与渐近性 总被引:2,自引:0,他引:2
计国君 《数学的实践与认识》1998,(2)
本文给出了一阶变系数滞后型微分方程振动解存在的积分条件,同时利用Banach不动点定理讨论了该类方程解的渐近性。 相似文献
12.
建立了偏差变元依赖于状态的三阶强迫泛函微分方程解的若干振动性和渐近性.所得结果是新的,同时推广了文献中的有关结果. 相似文献
13.
Consider the neutral delay differential equation [display math001] In this paper we are concerned with the asymptotic behavior and the oscillatory nature of solutions of Eq. (1). 相似文献
14.
带强迫项的二阶泛函微分方程解的振动性和渐近性 总被引:1,自引:0,他引:1
该文建立了偏差变元依赖于状态的二阶强迫泛函微分方程解的若干振动和渐近性质 ,所得结果推广和改进了文献中的有关结果 相似文献
15.
一类一阶中立型方程解的渐近性与振动性 总被引:1,自引:0,他引:1
讨论具有连续分布滞量的一阶中立型微分方程 ,(1)给出了非振动解当t→∞时收敛于零的充分条件和方程(1)所有解振动的判据。 相似文献
16.
17.
We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case λ ? 1 and if the corresponding second order differential equation h″ + q(t)h = 0 is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.
相似文献
$$x'''(t) + q(t)x'(t) + r(t)\left| x \right|^\lambda (t)\operatorname{sgn} x(t) = 0,{\text{ }}t \geqslant 0.$$
18.
Pavol Marušiak 《Journal of Differential Equations》1973,13(1):150-156
This paper consists of three theorems. The first theorem gives the asymptotic behavior of solutions of the nonlinear delay differential equation. The other theorems give sufficient conditions for oscillatory solutions of variants of that equation. 相似文献
19.
The authors obtain results on the asymptotic behavior of the non-oscillatory solutions of a first order nonlinear neutral delay differential equation. A theorem giving sufficient conditions for all bounded solutions to be oscillatory is also proved. 相似文献
20.
Sergio Albeverio Anne Boutet de Monvel-Berthier Zdzisław Brzeźniak 《Potential Analysis》1995,4(5):469-502
We develop an approach by finite dimensional approximations for the study of infinite dimensional oscillatory integrals and the relative method of stationary phase. We provide detailed asymptotic expansions in the nondegenerate as well as in the degenerate case. We also give applications to the derivation of detailed asymptotic expansions in Planck's constant for the Schrödinger equation. 相似文献