Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations

In this paper, we consider the following forced higher-order nonlinear neutral difference equation

     

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.     

Asymptotic behavior results for nonlinear neutral delay difference equations

This paper is concerned with the nonlinear neutral delay difference equation

(∗)     

Existence of bounded and unbounded nonoscillatory solutions of nonlinear partial difference equations

Consider the higher order nonlinear partial difference equation of neutral type

(∗)     

Asymptotic behavior of solutions of nonlinear neutral differential equations with impulses

This paper is concerned with a nonlinear neutral differential equations with impulses of the form

(*)     

Existence for nonoscillatory solutions of second-order nonlinear differential equations

In this paper, the existence of nonoscillatory solutions of the second-order nonlinear neutral differential equation

     

一类高阶非线性中立型差分方程组非振动解的存在性

研究了一类高阶非线性中立型差分方程组非振动解的存在性.利用Banach空间的压缩映象原理,获得了该方程组存在非振动解的充分条件.     

Asymptotic behavior of nonlinear difference systems

In this paper, we consider two-dimensional nonlinear difference systems of the form

We classify their solutions according to asymptotic behavior and give some necessary and sufficient conditions for the existence of solutions of such classes.     

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     

Bounded continuous nonoscillatory solutions of second-order nonlinear difference equations with continuous variable

In this paper, by using the fixed point theory, under quite general condition on the nonlinear term, we obtain an existence result concerning bounded continuous nonoscillatory solutions of a second-order nonlinear difference equation with continuous variable.     

Existence of nonoscillatory solutions to neutral dynamic equations on time scales

In this paper, we give an analogue of the Arzela-Ascoli theorem on time scales. Then, we establish the existence of nonoscillatory solutions to the neutral dynamic equation Δ[x(t)+p(t)x(g(t))]+f(t,x(h(t)))=0 on a time scale. To dwell upon the importance of our results, three interesting examples are also included.     

脉冲时滞差分方程非振动解的存在性

讨论脉冲时滞差分方程 给出了由时滞差分方程非振动解的存在性刻划出相应的脉冲时滞差分方程的同样性质的一般性脉冲条件。     

Asymptotic properties of solutions to linear non-autonomous neutral differential equations

In this article we study asymptotic properties of solutions to first order linear neutral differential equations with variable coefficients and constant delays. Results are stated in terms of the solution to a characteristic equation. By doing this, we extend some of the results obtained for delay equations in [J.G. Dix, Ch.G. Philos, I.K. Purnaras, An asymptotic property of solutions to linear non-autonomous delay differential equations, Electron. J. Differential Equations 2005 (2005) 1-9] to neutral equations.     

Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations

This paper considers a class of fourth order nonlinear difference equations Δ²(r _n Δ²(y _n ) + Δ²(r _n ,f(n,n _n )=0,n ∈N(n ₀) wheref(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory. Partially Supported by the National Science Foundation of China     

Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations

The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear difference equation of the form where m is even, is studied. Examples are included to illustrate the results.     

Linearized oscillations in nonlinear delay difference equations

Consider the nonlinear delay difference equation We establish a linearized oscillation result of this equation, which is the extension of the result in the paper [1]. Supported by the National Natural Science Foundation of China     

Asymptotic behavior of bounded solutions for a system of neutral functional differential equations

Consider the system of neutral functional differential equations

     

A note on the existence and asymptotic behavior of nonoscillatory solutions of fourth order quasilinear differential equations

This paper is concerned with nonoscillatory solutions of the fourth order quasilinear differential equation