@Article{Purushothaman2026,
author = "Purushothaman, Ganesh and Nandakumar, Pandarinathan and Chatzarakis, George E. and Thandapani, Ethiraju",
title = "Nonlinear hybrid second-order neutral delay differential equation with mixed sign terms: Oscillation via symmetry transform",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "4",
pages = "521--539",
doi = "https://doi.org/10.7494/OpMath.202606121",
url = "https://doi.org/10.7494/OpMath.202606121",
abstract = "This paper investigates the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations with both positive and negative terms of the form \[\left(a(\theta) z^{\prime}(\theta)\right)^{\prime} - p(\theta)x(\theta) + q(\theta)x^{\alpha}(\sigma(\theta)) = 0, \quad \theta \geq \theta_{0},\] where \(z(\theta) = x(\theta) + b(\theta)x(\tau(\theta))\). To facilitate the analysis, the equation is transformed, via a positive solution of an auxiliary second-order ordinary differential equation, into a binomial form. By employing the comparison and integral averaging techniques together with the arithmetic-geometric mean inequality, we establish new sufficient conditions for the oscillation of all solutions. The results obtained extend and improve several existing criteria in the literature. Finally, illustrative examples are presented to demonstrate the effectiveness, novelty, and applicability of the proposed oscillation criteria.",
keywords = "oscillation, second-order, neutral, delay differential equation, symmetry transform",
issn = "1232-9274"
}