scholarly journals Neutral Difference System and its Nonoscillatory Solutions

2018 ◽  
Vol 71 (1) ◽  
pp. 139-148
Author(s):  
Jana Pasáčková
Keyword(s):  
Difference Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Difference System ◽  
Nonlinear Difference Equations ◽  
Nonoscillatory Solutions ◽  
Weak Property ◽  
Property B

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.

scholarly journals Oscillatory and asymptotic behaviour of second order nonlinear difference equations

1996 ◽  
Vol 39 (3) ◽  
pp. 525-533 ◽  
Author(s):  
Bing Liu ◽  
Jurang Yan
Keyword(s):  
Asymptotic Behaviour ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Nonoscillatory Solutions ◽  
Asymptotic Behaviour Of Solutions ◽  
All Solutions ◽  
Image Position

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.

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

2001 ◽  
Vol 27 (2) ◽  
pp. 69-76 ◽  
Author(s):  
E. Thandapani ◽  
S. Lourdu Marian ◽  
John R. Graef
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Nonlinear Difference Equations ◽  
Nonoscillatory Solutions ◽  
Asymptotic Decay

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.

scholarly journals Existence of nonoscillatory solutions for system of neutral difference equations

2015 ◽  
Vol 9 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Małgorzata Migda ◽  
Ewa Schmeidel ◽  
Małgorzata Zdanowicz
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Neutral Difference Equations

The system of neutral type difference equations with delays {?(x(n) + p(n) x(n - ?))= a(n) f(y(n - l)) ?y(n) = b(n) g(z(n - m)) ?z(n) = c(n) h(x(n - k)) is considered. The aim of this paper is to present sufficient conditions for the existence of nonoscillatory bounded positive solutions of the considered system with various (p(n)).

scholarly journals On the oscillation of a nonlinear two-dimensional difference systems

2001 ◽  
Vol 32 (3) ◽  
pp. 201-209 ◽  
Author(s):  
E. Thandapani ◽  
B. Ponnammal
Keyword(s):  
Asymptotic Behavior ◽  
Sufficient Conditions ◽  
Real Sequence ◽  
Two Dimensional ◽  
Difference System ◽  
Nonoscillatory Solutions ◽  
Difference Systems ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Strongly Sublinear

The authors consider the two-dimensional difference system$$ \Delta x_n = b_n g (y_n) $$ $$ \Delta y_n = -f(n, x_{n+1}) $$where $ n \in N(n_0) = \{ n_0, n_0+1, \ldots \} $, $ n_0 $ a nonnegative integer; $ \{ b_n \} $ is a real sequence, $ f: N(n_0) \times {\rm R} \to {\rm R} $ is continuous with $ u f(n,u) > 0 $ for all $ u \ne 0 $. Necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior are given. Also sufficient conditions for all solutions to be oscillatory are obtained if $ f $ is either strongly sublinear or strongly superlinear. Examples of their results are also inserted.

scholarly journals On the Periodicity of General Class of Difference Equations

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 75 ◽  
Author(s):  
Osama Moaaz ◽  
Hamida Mahjoub ◽  
Ali Muhib
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Usual Method ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient

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.

scholarly journals Nonoscillatory Solutions for System of Neutral Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zhanhe Chen ◽  
Taixiang Sun ◽  
Qi Wang ◽  
Hongjian Xi
Keyword(s):  
Time Scales ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Functional System ◽  
Dynamic Equations ◽  
Nonoscillatory Solutions ◽  
Neutral Dynamic Equations

We will discuss nonoscillatory solutions to then-dimensional functional system of neutral type dynamic equations on time scales. We will establish some sufficient conditions for nonoscillatory solutions with the propertylimt→∞⁡xit=0, i=1, 2, …,n.

scholarly journals Necessary and Sufficient Conditions for Positive Solutions of Second-Order Nonlinear Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Zhi-Qiang Zhu
Keyword(s):  
Time Scales ◽  
Difference Equations ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations ◽  
Necessary And Sufficient Criteria ◽  
The Difference ◽  
Necessary And Sufficient

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.

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