一类N阶中立型微分系统非振动解的存在性

通过在有界连续函数集上构造压缩映射的方法,利用不动点理论定性地研究了一类n阶中立型微分系统非振动解的存在性,获得了这一类系统存在非振动解的充分条件.     

On a cyclic disconjugate operator associated to linear differential equations

In this paper the disconjugate linear differential operator of n-th order D^1/(n) given by $$D_1^{(n)} (x)(t) = \frac{1}{{a_n (t)}}\frac{d}{{dt}}\frac{1}{{a_{n - 1} (t)}} \ldots \frac{1}{{a_1 (t)}}\frac{d}{{dt}}x(t)$$ is considered together with other n?1 operators, which are obtained from D ₁ ⁽ⁿ⁾ by an ordered cyclic permutation of the functions a_i. Such operators play an important role in the study of oscillation of the associated linear differential equation (*) $$D_1^{(n)} (x)(t) \pm x(t) = 0.$$ Some properties of these operators suggest the new idea of «isomorphism of oscillation». The existence of an isomorphism of oscillation allows to describe the oscillatory or nonoscillatory behavior of solutions of (*) by the oscillatory or nonoscillatory behavior of solutions of other n ?1 suitable linear differential equations. From this fact one can easily obtain new results about oscillation or nonoscillation of (*) that might be hard to prove directly. Several interesting consequences concerning the classification of solutions of (*) are also presented together with some new applications to the structure of the set of nonoscillatory solutions of (*).     

Asymptotic behaviour and existence of nonoscillatory solutions of second-order neutral delay difference equations

In this paper, we give a classification of nonoscillatory solution of a second-order neutral delay difference equation of the form $$\Delta ^2 (x_n - c_n x_{n - \tau } ) = f(n, x_{g_1 (n)} ,..., x_{g_m (n)} ).$$ Some existence results for each kind of nonoscillatory solutions are also established.     

Preservation of nonoscillatory behavior of solutions of second-order delay differential equations under impulsive perturbations

We offer new criteria for the preservation of nonoscillatory behavior of solutions of the delay differential equation of second-order

under impulsive perturbations. A technique of direct analysis in this paper is developed.     

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.     

Classification and existence of nonoscillatory solutions of higher order nonlinear neutral difference equations

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $$\Delta ^r (x_n + px_{n - \tau } ) + f(n,x_{n - \sigma _1 (n)} ,x_{n - \sigma _2 (n)} ,...,x_{n - \sigma _m (n)} ) = 0.$$ We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.     

Nonprincipal solutions of half-linear second order differential equations

We consider the nonoscillatory half-linear second order differential equation

(∗)     

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.     

解守恒律方程组的一类新差分格式

初值问题(1.1)的一个主要特点是:即使初值函数w_0(x)是充分光滑的,大范围的古典解也不一定存在.用激波捕捉法(即“穿行”法)数值求解(1.1)通常精度较低.六十年代出现了一些二阶精度的差分格式.例如Lax-Wendroff格式.但这些格式的差分解通常在激波等间断附近产生较大的过头和低亏现象.本文用一个二阶精度的差分格式修正     

一类二阶中立型差分方程正解的渐近稳定性

研究了下列二阶中立型差分方程Δ2[x(n)-px(n-τ)]+q(n)x(g(n))=0,n n0正解渐近趋向于零的充分条件.     

Relaxation WENO schemes for multidimensional hyperbolic systems of conservation laws

We present a class of high‐order weighted essentially nonoscillatory (WENO) reconstructions based on relaxation approximation of hyperbolic systems of conservation laws. The main advantage of combining the WENO schemes with relaxation approximation is the fact that the presented schemes avoid solution of the Riemann problems due to the relaxation approach and high‐resolution is obtained by applying the WENO approach. The emphasis is on a fifth‐order scheme and its performance for solving a wide class of systems of conservation laws. To show the effectiveness of these methods, we present numerical results for different test problems on multidimensional hyperbolic systems of conservation laws. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A necessary and sufficient condition for nonoscillatory behavior of the solutions of a system of two linear equations of the first order

For the system y′=b(x) z, z′=?a (x)y, wherea (x), b(x)) ∈ c _[x0+∞), b(x)? 0 we obtain for x≥x₀a necessary and sufficient condition for nonoscillatory behavior. From this condition we derive new criteria for the nonoscillatory behavior of the system considered.     

Existence of nonoscillatory solutions of higher order neutral differential equations with distributed deviating arguments

In this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order linear neutral differential equations with distributed deviating arguments. We use the Banach contraction principle to obtain new sufficient conditions, which are weaker than those known, for the existence of nonoscillatory solutions.     

Decaying solutions for discrete boundary value problems on the half line

Some nonlocal boundary value problems, associated to a class of functional difference equations on unbounded domains, are considered by means of a new approach. Their solvability is obtained by using properties of the recessive solution to suitable half-linear difference equations, a half-linearization technique and a fixed point theorem in Frechét spaces. The result is applied to derive the existence of nonoscillatory solutions with initial and final data. Examples and open problems complete the paper.     

二阶中立型微分方程非振动解的存在性

考虑了一类变系数的具有强迫项的二阶中立型微分方程(x(t)+R(t)x(h(t)))″+P(t)x(g_1(t))-Q(t)x(g_2(t))=f(t)非振动解的存在性问题.通过Banach压缩映像原理,分别得到了方程存在满足■|x(t)|>0的非振动解x(t)的充分条件与必要条件,推广了一阶变系数方程的相应结果.     

The existence of nonoscillatory solutions of higher order nonlinear neutral equations

In this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order nonlinear neutral differential equations. Our results include as special cases some well-known results for linear and nonlinear equations of first, second and higher order. We use the Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.     

带强迫项高阶中立型微分方程的振动性和非振动性

我们给出一类强迫高阶非线性中立型时滞微分方程一切解振动的充分条件.而且,也研究了一类强迫一阶中立型方程非振动解的渐近性.     

时标上带强迫项高阶中立型动力方程的振动性与非振动解的存在性

给出时标上一类带强迫项高阶中立型动力方程一切解振动和非振动解存在的若干充分条件.所得结果推广了一些已有的结论.     

非线性中立型微分方程非振动解的渐近性

本文得到一类非线性中立型微分方程非振动解的渐近性     

具有脉冲扰动的非线性时滞微分方程

本文研究一类脉冲非线性时滞微分方程解的性质，讨论了其解的整体存在性及非振动解的渐近性，也给出了其所有解振动的充分条件．