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#3 – Oscillation Criteria For Unstable Second-Order Nonlinear Dynamic Equations With Mixed Type Deviating Arguments

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Gokula N. Chhatria, Said R. Grace, And J. R. Graef
Oscillation Criteria For Unstable Second-Order Nonlinear Dynamic Equations With Mixed Type Deviating Arguments
Dynamic Systems and Applications 35 (2026) 45-45

https://doi.org/10.46719/dsa2026.35.03

ABSTRACT.
The goal of this work is to establish new criteria for the oscillation of all solutions of the second-order dynamic equation with mixed arguments

(r(ν)yΔ(ν))Δ=q(ν)f(y(τ(ν))).\left(r(\nu)y^{\Delta}(\nu)\right)^{\Delta} = q(\nu) f(y(\tau(\nu))).

The approach used employs the existence of an suitable auxiliary function and integral averaging principles. This makes it possible to improve many existing criteria known for such equations. We note that the results presented here are new even in the cases where T = R and T = Z. The results are illustrated by some examples.

AMS (MOS) Subject Classification. 34C10, 34K11, 34N05, 39A10.

Key Words and Phrases. Oscillation, nonoscillation, dynamic equations, mixed arguments.

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