Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

Abstract

In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation).

Keywords

• half-linear differential equation
• oscillation criteria
• modified Riccati technique
• Euler-type equation
• second-order differential equation