Oscillation criteria for fourth-order neutral quasilinear differential equations in the noncanonical case

Abstract

This article investigates the monotonic properties and oscillatory behavior of quasi-linear fourth-order neutral differential equations in the noncanonical case. By establishing new monotonic properties for positive solutions, we derive refined relationships between the solutions and their associated auxiliary functions. Based on these results, effective oscillation criteria are obtained to ensure the oscillation of all solutions. The results are supported by illustrative examples and extend and improve several existing works, and provide a useful approach for studying more general classes of higher-order nonlinear neutral differential equations. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/24/abstr.html