TY  - JOUR
ID  - Purushothaman2026
LB  - Purushothaman2026
AU  - Purushothaman, Ganesh
AU  - Nandakumar, Pandarinathan
AU  - Chatzarakis, George E.
AU  - Thandapani, Ethiraju
TI  - Nonlinear hybrid second-order neutral delay differential equation with mixed sign terms: Oscillation via symmetry transform
ST  - Nonlinear hybrid second-order neutral delay differential equation with mixed sign terms: Oscillation via symmetry transform
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 4
SP  - 521
EP  - 539
DO  - https://doi.org/10.7494/OpMath.202606121
UR  - https://doi.org/10.7494/OpMath.202606121
AB  - 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.
KW  - oscillation
KW  - second-order
KW  - neutral
KW  - delay differential equation
KW  - symmetry transform
SN  - 1232-9274
ER  -