Oscillation of solutions of second-order linear differential equations and corresponding difference equations

Abstract

In this paper, we present conditions ensuring that solutions of linear second-order differential equations oscillate, provided solutions of corresponding difference equations oscillate. We also establish the converse result, namely, when oscillation of solutions of difference equations implies oscillation of solutions of corresponding differential equations.

Keywords::

• oscillation
• zeros of solutions
• difference equation
• finite difference
• amplitude of oscillation

Acknowledgements

This work is partially supported by the FFR of Ukraine under Grant No. 0113U003068. The authors would like to thank the referees for their careful reading of the manuscript and their valuable comments.