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1.
非线性高阶差分方程的振动性   总被引:10,自引:0,他引:10  
首先我们证明了下列两个差分方程在振动性上是等价的,其中,和都是整数,m是奇数,f是非减的且满足当时.其次,也得到了这些方程的新的振动准则  相似文献   

2.
奇数阶中立型差分方程的线性化振动性定理   总被引:3,自引:0,他引:3  
周展  庚建设 《应用数学》1999,12(4):65-68
本文得到了奇数阶中立型差分方程的一个线性化振动性定理,是Gy氹ri和Ladas在文[2]中所提公开问题的一个离散结果  相似文献   

3.
具有连续变量的差分方程振动性的判据   总被引:6,自引:0,他引:6  
借助研究离散变量的差分方程振动性的一般方法,本文建立了具有连续变量、变系数的差分方程振动性判据,其结果改进了文献[4]中的一些结果.  相似文献   

4.
一类二阶非线性中立型差分方程的振动性   总被引:1,自引:1,他引:0  
研究了二阶非线性中立型差分方程Δ2(xn+pxn-l)+qnf(xn-k)=0的振动性,获得了该类方程振动的三个充分性定理.所得结果将一阶非线性中立型差分方程已有振动性的相应结论推广到了二阶非线性中立型差分方程.  相似文献   

5.
研究了二阶中立型变时滞差分方程Δ2(xn+pxn-l)+qnf(xσ(n))=0解的振动性,获得了该类方程全部非平凡解振动的三个定理.所得结果将二阶中立型差分方程已有的振动性的相应结论推广到了二阶中立型变时滞差分方程.  相似文献   

6.
本文考虑一类非线性延迟微分方程-带有单峰造血率的造血模型数值解的振动性及非振动性。运用线性化理论,把非线性差分方程的振动性转化为其对应的线性差分方程的振动性,通过判断线性方程的特征方程根的情况,得到了非线性差分方程振动和存在非振动解的充分条件。对于非振动的数值解,证明了非振动的数值解最终都趋于方程的平衡解。为了更有力的说明我们的结果给出了相应的算例.  相似文献   

7.
具有连续变量的差分方程振动性的判据   总被引:59,自引:1,他引:59  
张玉珠  燕居让 《数学学报》1995,38(3):406-411
本文借助研究离散变量的差分方程振动性的一般方法,建立了具有连续变量、变系数的差分方程振动性判据,并给出了具体例子。  相似文献   

8.
研究具有可变时滞的非自治中立型差分方程Δ(xn-cxn-k)+h(n,xn-ln)=0,n=0,1,2,…的振动性,得到了这类差分方程振动的必要条件、充分条件和充要条件,同时得到了这类方程的最终正解存在性判据.  相似文献   

9.
二阶中立型差分方程的振动性   总被引:11,自引:0,他引:11  
研究了一类变系数的二阶中立型时滞差分方程的振动性,得到了该类方程振动及解的一阶差分振动的充分条件。  相似文献   

10.
具有可变时滞的非线性非自治差分方程的振动性及其应用   总被引:9,自引:0,他引:9  
本文获得了一类具有可变时滞的非线性非自治差分方程的振动准则,建立了这类差分方程的几个线性化振动性定理,并得到了具有可变时滞的离散型非自治广义Logistic方程关于其正平衡点振动的一系列充分条件.  相似文献   

11.
12.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

14.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

17.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].  相似文献   

18.
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.  相似文献   

19.
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with  相似文献   

20.
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