About an unsolved stability problem for a stochastic difference equation with continuous time

An unsolved problem of stability for stochastic difference equation with continuous time is proposed for consideration.     

Asymptotic behavior of a differential equation with distributed delays

In this paper, sufficient conditions are established for the asymptotical behavior of solutions of the delay differential equation

x^′(t)=F(t,xt)+G(t,xt)     

Asymptotic behavior of solutions of linear homogeneous second-order difference equations

We analyze and study the asymptotic behavior (asn→∞) of the general solutionx _n of the equationx _n+2 =Ax _n +Bx _n+1 ,A≠0,n=0,1,2,..., for various possible values of coefficients and initial data. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 211–215, August, 99.     

Asymptotic behavior of a nonlinear delay difference equation

This paper considers a class of nonlinear difference equations

Δ₃y_n + ƒ(n, y_n, y_n−r) = 0, n N (n₀)

. A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given.     

Asymptotic behavior of solutions of difference equations in Banach spaces

In this paper we consider the first order difference equation

and give necessary and sufficient conditions so that there exist solutions which are asymptotically constant. These results generalize those given earlier by Popenda and Schmeidel. As an application we give necessary and sufficient conditions for the second order difference equation

to have asymptotically constant solutions.

     

Asymptotic behavior of solutions for a class of retarded difference equations

Consider the retarded difference equationx _n −x _n−1 =F(−f(x _n )+g(x _n−k )), wherek is a positive integer,F,f,g:R→R are continuous,F andf are increasing onR, anduF(u)>0 for allu≠0. We show that whenf(y)≥g(y) (resp. f(y)≤g(y)) fory∈R, every solution of (*) tends to either a constant or −∞ (resp. ∞) asn→∞. Furthermore, iff(y)≡g(y) fory∈R, then every solution of (*) tends to a constant asn→∞. Project supported by NNSF (19601016) of China and NSF (97-37-42) of Hunan     

Asymptotic behavior of the solutions of the p -Laplacian equation

The asymptotic behavior of the solutions for p-Laplacian equations as p → ∞ is studied.     

可和系数的二阶差分方程解的渐近性

考虑非线性差分方程△(Pn-1△（yn-1)^σ） qnf(yn)=0,n=1,2,3…其中linn→∞∑s=1^nqs存在且为有限给出了方程（E）具有渐近于非零常数解的必要（充分）条件。     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

Global behavior for a fourth-order rational difference equation

In this paper, we use a method different from the known literature to investigate the global behavior of the following fourth-order rational difference equation:

     

非线性时滞差分方程的全局吸引性

得到了具有多重时滞非线性差分方程x(n 1)-x(n) ∑i=1^k pi(n)fi(x(gi(n)))=0,n=0,1,2,…的每个解趋于零的充分条件。     

Large time behavior of solutions to a class of doubly nonlinear parabolic equations

We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u _t = div(u ^m−1|Du| ^p−2 Du) − u ^q with an initial condition u(x, 0) = u ₀(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2. The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei University in China.     

Asymptotic behavior results for nonlinear neutral delay difference equations

This paper is concerned with the nonlinear neutral delay difference equation

(∗)     

Qualitative properties for a fourth-order rational difference equation

In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational difference equation:

     

具强迫项高阶非线性中立型差分方程的振动性与渐近性

讨论具强迫项高阶非线性中立型差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=fn,n=0,1,2,…及其相关联的差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=0,n=0,1,2,…的振动性与渐近性,得到了所有解振动或趋于零的充分性判据.     

Long time behavior of the Fokker-Planck-Boltzmann equation

This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian.