Yutaka Shoukaku
Comparison Theorems for Second Order Linear and Half-Linear Difference Equations
Dynamic Systems and Applications 33 (2024)    59-72

https://doi.org/10.46719/dsa2024.33.03

ABSTRACT.
In this paper, discrete comparison theorems of Sturm’s type is developed for a pair of second order linear difference equations. In particular, we present here Sturm-Picone type and Leighton type comparison theorems on second order linear difference equations. Our research is motivated by famous book [15] dealing with a similar problem for second order linear differential equations. Furthermore we extend and investigate the more general half-linear difference equation by referring the famous paper [10]. Examples are given to illustrate the relevance of the results.

AMS (MOS) Subject Classification. 34C10, 34C15, 34K40.
Key Words and Phrases. Oscillation, comparison theorem, difference equation.