Nonlinear equations of fourth-order with 𝑝-Laplacian like operators: Oscillation, methods and applications

Abstract

Fourth-order differential equations appear in physical applications (such as fluid dynamics, electromagnetism, quantum mechanics). The aim of this work is to study oscillatory behavior of solutions for a fourth-order neutral nonlinear differential equation, driven by app-Laplace differential operator. Some oscillation criteria for the understudy equation have been obtained by the theory of comparison. The obtained results improved the well-known oscillation results presented in the literature. An example is illustrated to show the applicability of the obtained results.