scholarly journals Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations

Author(s):  
E. Thandapani ◽  
S. Lourdu Marian ◽  
John R. Graef

The authors consider themth order nonlinear difference equations of the formDmyn+qnf(yσ(n))=ei, wherem≥1,n∈ℕ={0,1,2,…},ani>0fori=1,2,…,m−1,anm≡1,D0yn=yn,Diyn=aniΔDi−1yn,i=1,2,…,m,σ(n)→∞asn→∞, andf:ℝ→ℝis continuous withuf(u)>0foru≠0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero asn→∞without assuming that∑n=0∞1/ani=∞,i=1,2,…,m−1,{qn}is positive, oren≡0as is often required. If{qn}is positive, they prove another such result for all nonoscillatory solutions.

2018 ◽  
Vol 71 (1) ◽  
pp. 139-148
Author(s):  
Jana Pasáčková

Abstract The paper deals with a system of four nonlinear difference equations where the first equation is of a neutral type. We study nonoscillatory solutions of the system and we present sufficient conditions for the system to have weak property B.


1996 ◽  
Vol 39 (3) ◽  
pp. 525-533 ◽  
Author(s):  
Bing Liu ◽  
Jurang Yan

In this paper we are dealing with oscillatory and asymptotic behaviour of solutions of second order nonlinear difference equations of the formSome sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) is considered also.


Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 75 ◽  
Author(s):  
Osama Moaaz ◽  
Hamida Mahjoub ◽  
Ali Muhib

In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.


2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Zhi-Qiang Zhu

This paper is concerned with the existence of nonoscillatory solutions for the nonlinear dynamic equation on time scales. By making use of the generalized Riccati transformation technique, we establish some necessary and sufficient criteria to guarantee the existence. The last examples show that our results can be applied on the differential equations, the difference equations, and the -difference equations.


2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Zhijian Wei ◽  
Meitao Le

We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.


2018 ◽  
Vol 14 (2) ◽  
pp. 7975-7982
Author(s):  
Danhua He

In this paper, a class of nonlinear difference equations with time-varying delays is considered. Based on a generalized discrete Halanay inequality, some sufficient conditions for the attracting set and the global asymptotic stability of the nonlinear difference equations with time-varying delays are obtained.


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