A survey on oscillation of linear delay difference equations

2004 ◽  
pp. 57-73
Author(s):  
X. Qian ◽  
Z. Wang
Keyword(s):  
Difference Equations ◽  
Linear Delay ◽  
Delay Difference Equations ◽  
Delay Difference

scholarly journals Nontrivial periodic solutions to delay difference equations via Morse theory

2018 ◽  
Vol 16 (1) ◽  
pp. 885-896 ◽  
Author(s):  
Yuhua Long ◽  
Haiping Shi ◽  
Xiaoqing Deng
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Morse Theory ◽  
Sufficient Conditions ◽  
Asymptotically Linear ◽  
Linear Delay ◽  
Nontrivial Periodic Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4T + 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.

scholarly journals Stability conditions for linear delay difference equations: a survey and perspectives

2015 ◽  
Vol 63 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Jan Čermák
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Stability Conditions ◽  
Linear Delay ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Theoretical Results

Abstract The paper presents an overview of the basic results and methods for stability investigations of higher-order linear autonomous difference equations. The presented criteria formulate several types of necessary and sufficient conditions for the asymptotic stability of the zero solution of studied equations, with a special emphasize put on delay difference equations. Various comments, comparisons, examples and illustrations are given to support theoretical results.

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