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Analysis of Oscillatory Behavior of Second-Order Neutral Delay Difference Equations

Author

Listed:
  • K. Masaniammal

    (Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi 642003, Tamil Nadu, India)

  • R. Ramesh

    (Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi 642003, Tamil Nadu, India)

  • L. Senthil Kumar

    (Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi 642003, Tamil Nadu, India)

  • K. Kalaiselvi

    (Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi 642003, Tamil Nadu, India)

  • Vadivel Rajarathinam

    (Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand)

  • Taha Radwan

    (Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia)

Abstract

The paper investigates the oscillation, zero-convergence, and solutions of second-order neutral delay difference equations containing three nonlinear delayed terms with different growth rates. By using positivity and monotonicity conditions on an auxiliary function along with divergence-type conditions on the coefficient sequences of the neutral and delayed terms, the paper establishes new criteria that guarantee oscillation or convergence of all solutions. These novel findings extend and enhance several of the existing oscillation criteria established by the literature. Suggestions for further investigation are included with illustrative examples.

Suggested Citation

  • K. Masaniammal & R. Ramesh & L. Senthil Kumar & K. Kalaiselvi & Vadivel Rajarathinam & Taha Radwan, 2025. "Analysis of Oscillatory Behavior of Second-Order Neutral Delay Difference Equations," Mathematics, MDPI, vol. 13(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:24:p:3902-:d:1811706
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