scholarly journals Comparison theorems of oscillation and nonoscillation for neutral difference equations with continuous arguments

2003 ◽  
Vol 2 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Xianyi Li ◽  
◽  
Deming Zhu ◽  
Keyword(s):  
Difference Equations ◽  
Comparison Theorems ◽  
Neutral Difference Equations ◽  
Oscillation And Nonoscillation

scholarly journals OSCILLATION AND COMPARISON THEOREMS FOR NEUTRAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (4) ◽  
pp. 343-352
Author(s):  
B. G. ZHANG ◽  
PENGXIANG YAN
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Comparison Theorems ◽  
Qualitative Properties ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Riccati Techniques ◽  
Qualitative Properties Of Solutions

In this paper we study qualitative properties of solutions of the neutral difference equation $$ \Delta(y_n-py_{n-k})+\sum_{i=1}^m q_n^i y_{n-k_i} =0 $$ $$ y_n=A_n \quad \text{ for } n=-M, \cdots, -1, 0$$ where $p \ge 1$, $M =\max\{k, k_1, \cdots, k_m\}$, and $k$, $k_i$, $i =1, \cdots, m$, are nonnegative integers. Riccati techniques are used.  

scholarly journals Oscillation and comparison theorems for certain neutral difference equations

1992 ◽  
Vol 34 (2) ◽  
pp. 245-256 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Comparison Theorems ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
Arbitrary Sign ◽  
Image Position ◽  
Mixed Arguments

AbstractSome comparison theorems and oscillation criteria are established for the neutral difference equationas well as for certain neutral difference equations with coefficients of arbitrary sign. Neutral difference equations with mixed arguments are also considered.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

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