Open Access"Oscillations of second-order noncanonical advanced difference equations via canonical transformation"
Author(s) -
George E. Chatzarakis,
N. Indrajith,
Spiros Panetsos,
E. Thandapani
Publication year - 2022
Publication title -
carpathian journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.812
H-Index - 25
eISSN - 1843-4401
pISSN - 1584-2851
DOI - 10.37193/cjm.2022.02.09
Subject(s) - oscillation (cell signaling) , monotonic function , integer (computer science) , mathematics , order (exchange) , sigma , transformation (genetics) , sequence (biology) , combinatorics , mathematical physics , mathematical analysis , physics , quantum mechanics , computer science , chemistry , biochemistry , finance , economics , gene , programming language
"This paper introduces a new improved method for obtaining the oscillation of a second-order advanced difference equation of the form \begin{equation*} \Delta(\eta(n)\Delta\chi(n))+f(n)\chi(\sigma(n))=0 \end{equation*} where $\eta(n)>0,$ $\sum_{n=n_0}^{\infty}\frac{1}{\eta(n)} 0,$ $\sigma(n)\geq n+1,$ and $\{\sigma(n)\}$ is a monotonically increasing integer sequence. We derive new oscillation criteria by transforming the studied equation into the canonical form. The obtained results are original and improve on the existing criteria. Examples illustrating the main results are presented at the end of the paper."