Oscillatory solutions of nonlinear fourth order differential equations with a middle term

Abstract

We study the oscillation of a fourth order nonlinear differential equation with a middle term. Using a certain energy function, we describe the properties of oscillatory solutions. The paper extends oscillation criteria stated for equations with the operator $x^{(4)} + x''$ and completes the results stated for super-linear and sub-linear case. Oscillation results are new also for the linear equation.

Keywords

• fourth order nonlinear differential equation
• oscillatory solution
• oscillation