On the oscillation of certain fourth-order differential equations with p-Laplacian like operator

Abstract

• Oscillation of certain fourth order differential equations. • To study the oscillatory properties of fourth order delay differential equations. • Comparison with first and second order differential equations and Riccati transformations. The aim of this work is to study the oscillatory properties of the solutions of fourth-order delay differential equations with a p -Laplacian like operator of the form ( r ( ν ) | w ″ ′ ( ν ) | p 1 − 2 w ″ ′ ( ν ) ) ′ + q ( ν ) | w ( η ( ν ) ) | p 2 − 2 w ( η ( ν ) ) = 0 . The results obtained are based on the comparison with first and second-order differential equations and the use of a Riccati transformation. Some examples are provided to illustrate the main results.