On Non-Negative Measurable Solutions of a Difference Functional Equation

Following M. Laczkovich [5] we consider the iterative functional equation

p-Laplace型非线性泛函差分方程正解的存在性

作者研究下述的p-Laplace型非线性泛函差分方程边值问题正解和多重正解的存在性,得到相应的充分条件,其中Φp(u)=|u|p-2u,P>1,(?)(0)= 0,C+={(?):(?)∈ C,(?)(k)≥0,k∈[-r,0])．     

一类非自治非线性时滞差分方程正解的振动性

研究了一类非自治非线性时滞差分方程△xn=rnxn1-xn-k/1-cxn-k的正确解关于平衡点1的振动性,所获结果改进和推广了献[6]中的相关结论。     

Asymptotically Constant Solutions of Functional Difference Systems

We consider the functional difference system ( A ) j x i ( n )= f i ( n ; X ), 1 h i h k , where X =( x 1 ,…, x k ) and f 1 (·; X ),…, f k (·; X ) are real-valued functionals of X , which may depend quite arbitrarily on values of X ( l ) for multiple values of l ] Z . We give sufficient conditions for ( A ) to have solutions that approach specified constant vectors as n M X . Some of the results guarantee only that the solutions are defined for n sufficiently large, while others are global. The proof of the main theorem is based on the Schauder-Tychonoff theorem. Applications to specific quasi-linear systems are included.     

一类非自台非线性时滞差分方程正解的振动性

研究了一类非自治非线性时滞差分方程的正解关于平衡点l的振动性,所获结果改进和推广了文献[6]中的相关结论.     

非线性泛函差分方程解的性质

In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.     

On Stability of Solutions to One Class of Nonlinear Difference Systems

We consider some class of systems of nonlinear ordinary differential equations. We adjust the difference schemes corresponding to the equations under study in order to guarantee agreement between differential and difference systems in the sense of stability of the zero solution. We obtain conditions under which perturbations do not violate the asymptotic stability of solutions to difference systems.     

一类二阶非线性差分方程解的渐近性质

研究了一类二阶非线性差分方程解的渐近性质,应用分析方法,建立了两个新的渐近性定理.     

Finite-Dimensional Integrable Hamiltonian Systems Related to the Nonlinear Schrödinger Equation

A complete treatment of the binary nonlinearizations of spectral problems of the nonlinear Schrödinger (NLS) equation with the choice of distinct eigenvalue parameters is presented. Two kinds of constraints between the potentials and the eigenfunctions of the NLS equation are considered. From the first constraint, a pair of new finite-dimensional completely integrable Hamiltonian systems which constitute an integrable decomposition of the NLS equation are obtained. From the second constraint, a novel finite-dimensional integrable Hamiltonian system, which includes the system of multiple three-wave interaction as a special case, is obtained. It is found that the eigenvalue parameters real or not can lead to completely different symplectic structures of the restricted NLS flows. In addition, a relationship between the binary restricted Ablowitz–Kaup–Newell–Segur flows and the restricted NLS flows is revealed.     

Holomorphic Solutions of Some Functional Equations II

We study a certain type of functional equation, which is of significance from the view point of systems of difference equations. Let the characteristic values of the system be and The case that either || > 1 or 0 < || < 1 has been treated in a former paper. The case that = 1, || = 1 with 1 will be given in another paper. The present note deals with the case = = 1, the most difficult case.AMS Subject Classification (1991): 39A10 39B05     

一类非线性反应扩散方程及方程组的分数步长差分格式

对一类反应扩散方程及方程组的初边值问题提出分数步长差分格式．利用高阶差分算子的分解,以及先验估计的理论和技巧,得到次优阶ｌ２ 误差估计．     

非线性边界条件下二阶奇异差分方程的正解

本文我们考虑如下二阶奇异差分边值问题\begin{equation*}\begin{cases}-\Delta^{2} u(t-1)=\lambda g(t)f(u) ,\ t\in [1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{cases}\end{equation*}正解的存在性. 其中, $\lambda>0$, $f:(0,\infty)\rightarrow \mathbb{R}$ 是连续的,且允许在~$0$ 处奇异.通过引入一个新的全连续算子, 我们建立正解的存在性.     

一类高阶差分方程周期解的存在性

本文应用临界点理论获得了一类高阶差分方程k∑i=0(xn-i xn i) f(xn 1,xn,xn-1) =0, n∈z,k∈N非平凡M-周期解存在的充分条件.     

On Solutions to Riemann's Functional Equation

In 1921 Hamburger proved that Riemann's functional equation characterizes the Riemann zeta function in the space of functions representable by ordinary Dirichlet series satisfying certain regularity conditions. We consider solutions to a more general functional equation with real weight k. In the case of Hamburger's theorem, k = . We show that, under suitable conditions, the generalized functional equation admits no nontrivial solutions for k > 0 unless k = . Our proof generalizes an elegant proof of Hamburger's theorem given by Siegel, and employs a generalized integral transform.1997 Sunrise Way     

Exact Solutions to One Nonlinear Sobolev Equation

Moscow University Computational Mathematics and Cybernetics - Several families of exact solutions expressed in terms of elementary and special functions are constructed for one nonlinear...     

Monotone Solutions of a Higher-Order Neutral Difference Equation

A real sequence x _k is said to be (*)-monotone with respect to a sequence p _k and a positive integer if x _k > 0 and . This paper is concerned with the existence of (*)-monotone solutions of a neutral difference equation. Existence criteria are derived by means of a comparison theorem and by establishing explicit existence criteria for positive and/or bounded solutions of a majorant recurrence relation.     

一类非线性差分方程的整体收敛性

利用[5]中的证明方法给出了一类非线性差分方程整体收敛性的一个充分条件,并将[1],[5]中的结果推广到更为一般的情形.