# Oscillation conditions of the second-order noncanonical difference equations

Volume 25, Issue 4, pp 351--360
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.

### Share and Cite

##### ISRP Style

P. Gopalakrishnan, A. Murugesan, C. Jayakumar, Oscillation conditions of the second-order noncanonical difference equations, Journal of Mathematics and Computer Science, 25 (2022), no. 4, 351--360

##### AMA Style

Gopalakrishnan P., Murugesan A., Jayakumar C., Oscillation conditions of the second-order noncanonical difference equations. J Math Comput SCI-JM. (2022); 25(4):351--360

##### Chicago/Turabian Style

Gopalakrishnan, P., Murugesan, A., Jayakumar, C.. "Oscillation conditions of the second-order noncanonical difference equations." Journal of Mathematics and Computer Science, 25, no. 4 (2022): 351--360

### Keywords

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

•  39A10
•  39A12

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