Oscillation criteria for advanced fourth-order differential equations with mixed nonlinearities of Swift–Hohenberg type

Abstract This paper investigates the oscillatory behavior of solutions to a class of advanced fourth-order differential equations inspired by the Swift–Hohenberg model, incorporating multiple nonlinear terms. First, by assuming the nonoscillatory nature of an associated second-order linear differential equation along with an arithmetic-geometric mean inequality, the studied equation transformed to a compact form. Then, employing the comparison principle and the integral averaging technique some new sufficient criteria for the oscillation of all solutions are derived. Our results encompass equations with mixed nonlinearities and advanced arguments, broadening the existing oscillation theory. Three illustrative examples demonstrate the significance and novelty of our main findings, offering valuable tools for analyzing complex physical and biological systems modeled by such higher-order nonlinear differential equations.