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1.
在这篇文章内我们证明了一类线性积分方程存在唯一解.并给出解的表示式.它以Fredholm方程和Volterra方程为特殊情形.  相似文献   

2.
研究一类非线性无界时滞差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了有关的结果。  相似文献   

3.
一类非线性差分方程正解的不存在性   总被引:2,自引:1,他引:1  
本文研究一类非线性差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了[1]的结果。  相似文献   

4.
讨论了R∧N上带负扰动的临界非齐次多重调和方程的多解存在性,首先由泛函弱连续性方法获得方程的第一个解,再由山路引理获得方程的第二个解,本文的这种求解方法和这些结果不仅适用于R∧N上的二阶椭圆方程,而且也适用于尚未解决的R∧N上的双调和方程。  相似文献   

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具偏差变元的Lienard型方程的周期解   总被引:17,自引:0,他引:17  
在本文中,Lienard型方程具有周期解存在性的结果推广到具偏差变元的Lienard型方程。  相似文献   

6.
周宗福 《数学研究》2001,34(3):282-286
研究一类非线性高阶中立型差分方程的振动性,给出了该方程振动的几个充分条件,改进,扩展了[4]的有关结果。  相似文献   

7.
雷锦志  晏平 《应用数学》2003,16(3):75-81
本文使用微分代数的技巧,研究了发展方程的守恒率与对应的行波所满足方程的首次积分之间的关系.通过文本给出的结果,我们研究了Burgers方程和Burgers—KdV方程的可积性,证明了这两类方程都只有一个守恒率.利用本文给出的方法,可以通过常微分方程的研究方法来研究某些非线性发展方程.  相似文献   

8.
一般Lyness方程的周期性与严格振动性   总被引:3,自引:0,他引:3  
研究了一般的Lyness方程xn+1=xn/「(a+bxn)xn-1」,n=1,2,3,…,其中a、b∈「0,∞)且a+b〉0,初值x-1、x0为任意正数。得到了一些新的结果:方程(*)解的周期性的一个必要充分条件;方程(*)的所有解严格振动的充分条件。作为应用,解决了G.Ladas提出的一个公开问题。  相似文献   

9.
一类非线性方程的解的存在性及其应用   总被引:13,自引:0,他引:13  
许绍元 《应用数学》2000,13(1):23-26
设A是Amann意义下的凹(凸)算子,本文提出序Lipschitz条件,无需考虑任何紧性或连续性条件,由Mann迭代技巧证明了方程Ax=x的解的存在性,将所得结果应用于无辊域ammerstein发方程,得到了新结果。  相似文献   

10.
张玉珠  燕居让 《数学杂志》1995,15(3):340-344
本文研究了时滞Logistic方程与不等式关于方程平衡占的振动与非振动解的渐近性问题,得到了一些新的充分条件。本文的结果推广并改进了若干已知的定理。  相似文献   

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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.
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   

14.
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   

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.
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).  相似文献   

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