Oscillation conditions of the second-order noncanonical difference equations

Volume 25, Issue 4, pp 351--360 http://dx.doi.org/10.22436/jmcs.025.04.05

Publication Date: August 12, 2021 Submission Date: April 07, 2021 Revision Date: June 09, 2021 Accteptance Date: July 05, 2021

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Authors

P. Gopalakrishnan - Department of Mathematics, Mahendra Arts \(\&\) Science College (Autonomous), Kalipatti, Namakkal Dt., Tamil Nadu, India. A. Murugesan - Department of Mathematics, Government Arts College (Autonomous), Salem-636007, Tamil Nadu, India. C. Jayakumar - Department of Mathematics, Mahendra Arts \(\&\) Science College (Autonomous), Kalipatti, Namakkal Dt., Tamil Nadu, India.

Abstract

We derive new oscillatory conditions for the second-order noncanonical difference equations of the type \[ \Delta ( r(\nu) \Delta x(\nu) ) + q(\nu) x (\nu+\sigma) = 0, \quad \nu\geq \nu_0,\] by creating monotonical properties of nonoscillatory solutions. Our oscillatory outcomes are effectively an extension of the previous ones. We provide several examples to demonstrate the efficacy of the new criteria.

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Keywords

• Oscillation
• nonoscillation
• second-order
• canonical
• noncanonical
• delay
• difference equations

MSC

•  39A10
•  39A12

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