Paper Title:

Oscillation Criteria for Second Order Delay Difference Equations via Canonical Transformations and Some New Monotonic Properties

Author(s):

R. Deepalakhmi, S. Saravanan, J. R. Graef, and E. Thandapani

Department of Interdisciplinary Studies
Tamil Nadu Dr. Ambedkar Law University
Chennai-600113,
India.
profdeepalakshmi@gmail.com

Madras School of Economics,
Chennai-600025,
India.
profsaran11@gmail.com

Department of Mathematics,
University of Tennessee at Chattanooga,
Chattanooga,TN 37403,
USA.
john-graef@utc.edu

Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
ethandapani@yahoo.co.in

Abstract:

This paper is concerned with second-order linear noncanonical delay difference equations of the form

Δ(μ(t)Δ y(t))+ p(t)y(φ(t))=0.

The authors prove new oscillation criteria by first transforming the equation into canonical form and then obtaining some new monotonic properties of the positive solutions of the transformed equation. By using a comparison with first-order delay difference equations and a generalization of a technique developed by Koplatadze, they obtain their main results. Examples illustrating the improvement over known results in the literature are presented.

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