二阶泛函微分方程的振动性质

在本文中，我们研究了一类较广泛的二阶非线性泛函微分方程的振动性质。文中指出，在一定条件下，方程的非振动解仅有两类，而且给出了每一类非振动解存在的必要条件，同时也建立了方程振动的若干充分判据。     

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

ＯＳＣＩＬＬＡＴＩＯＮＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＩＭＰＵＬＳＥＳＳｈｅｎＪｉａｎｈｕａ（申建华）＆ＷａｎｇＺｈｉｃｈｅｎｇ（王志成）（ＨｕｎａｎＵｎ...     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

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.     

Oscillation of second‐order perturbed differential equations

We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On oscillatory solutions of quasilinear differential equations

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.     

Oscillatory retarded functional systems

This note is concerned with the oscillatory behavior of a linear retarded system. Several criteria are obtained for having the system oscillatory. Conditions regarding the existence of nonoscillatory solutions are also given.     

Nth Order extension of the Wintner–Leighton theorem

Sufficient conditions are given for the existence of oscillatory and nonoscillatory solutions of a class of nth order linear differential equations. These results include an extension of the Wintner–Leighton Theorem.     

高阶泛函微分方程的振动性质*

本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程的振动性质.文中指出.在一定条件下,方程的非振动解仅有两类,而且给出了每一类非振动解存在的必要条件,同时也建立了方程振动的若干充分判据.     

一阶中立型泛函微分方程解的渐近性与振动性

本文研究具有变系数和多偏差的一阶中立型微分方程，讨论了方程的非振动解的渐近性，得到了方程振动的充分判据，其中有些是变号系数的情形．     

STABILITY OF SOLUTIONS OF FIRST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH OSCILLATORY COEFFICIENTS

ＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＯＦＦＩＲＳＴＯＲＤＥＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＯＳＣＩＬＬＡＴＯＲＹＣＯＥＦＦＩＣＩＥＮＴＳ￥ＷａｎｇＱｉｒｕ(王其如）（ＬｕｏｙａｎｇＴｅａｃｈｅｒ?..     

ASYMPTOTICS AND OSCILLATION FOR FIRST ORDER MIXED NEUTRAL DIFFERENTIAL EQUATIONS

1IntroductionConsidertheneutraldifferentialequationswherepiERfori=l,2,...,m;o相似文献   

Oscillation,nonoscillation, and growth of solutions of nonlinear functional differential equations of arbitrary order

This paper discusses the growth and oscillatory behavior of solutions of n-th-order nonlinear functional differential equations. Sufficient conditions for all solutions or all bounded solutions to be nonoscillatory are given. An extensive bibliography is also included.     

脉冲时滞微分方程解的整体存在唯一性、振动性与非振动性

本文讨论脉冲时滞微分方程X’(t)=f(t,x(t-T_1(t)),…,x(t-T_n(t))),x(t_k)-x(t_k~-)=I_k(x(t_k~- )).获得了方程(E) 解的一个整体存在唯一性定理.当(E)是线性方程时,给出了由时滞微分方程解的振动性或非振动性刻划出相应的脉冲时滞微分方程的同样性质的一般性脉冲条件.     

Oscillation Criteria for Four-Dimensional Time-Scale Systems

In this paper, we obtain oscillation and nonoscillation criteria for solutions to four-dimensional systems of first-order dynamic equations on time scales. Especially, we are interested in the conditions which insure that every solution is oscillatory in the sub-linear, half-linear, and super-linear cases. Our approach is based on the sign of the components of nonoscillatory solutions. Several examples are included to highlight our main results.     

OSCILLATIONS OF FIRST ORDER NONLINEAR RETARDED DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＳＯＦＦＩＲＳＴＯＲＤＥＲＮＯＮＬＩＮＥＡＲＲＥＴＡＲＤＥＤＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＷａｎｇＱｉｒｕ（王其如）（ＬｕｏｙａｎｇＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，洛阳师范高等专科学校，邮编：４７１０２２）Ａｂｓ...     

Concerning solutions of third order self-adjoint differential equations

Summary This work is concerned with the behavior of solutions of third order self-adjoint differential equations. It is well known that products of solutions of a second order self-adjoint equation are solutions of the third order equation. A converse of this fact is established. Existence of oscillatory solutions and asymptotic behavior of nonoscillatory solutions is established. Separation and comparison theorems are obtained for such equations. Entrata in Redazione il 13 aprile 1972.     

On the behavior of the oscillatory solutions of first or second order delay differential equations

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.     

Stability of oscillatory solutions of differential equations with general piecewise constant arguments of mixed type

We examine scalar differential equations with general piecewise constant arguments of mixed type, in short DEPCAG of mixed type, that is, the arguments are general step functions. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Our results are new, extend and improve earlier publications. Several numerical examples and simulations are also given to show the feasibility of our results.     

Nonoscillatory solutions of forced second order linear equations. - II

Summary The number of nonoscillatory solutions of a forced second order linear differential equation is studied under the hypothesis that the homogeneous equation is oscillatory. The main technique involves expressing a general solution of the forced equation in terms of two parameters, given a pair of independent solutions of the homogeneous equation (see (2.4) below).     

A stability criterion for a neutral difference equation with delay

A stability criterion for a neutral difference equation with delay is established which extends and improves a result of Ladas et al. [1]. Our derivation is based on Lyapunov's direct method for stability, and avoids the approach employed by Ladas et al. who had considered asymptotic behaviors of oscillatory and nonoscillatory solutions.