Oscillation criteria for third-order nonlinear differential equations involving a sublinear neutral term and distributed deviating arguments

Abstract This study presents ground-breaking oscillation criteria for third-order nonlinear differential equations featuring a sublinear neutral term and distributed deviating arguments. By employing the generalized Riccati transformation, comparison principles and integral averaging techniques, we reveal novel insights into the asymptotic behavior of these complex differential equations. Moreover, the paper furnishes several examples to explicitly illustrate and validate the main theoretical findings, thereby offering valuable references and extensions for research in related fields. Our findings not only advance theoretical understanding but also hold promise for practical applications across diverse fields. This concise yet influential research offers a fresh perspective on the dynamical properties of higher-order neutral equations.