Half-linear Euler differential equation and its perturbations

Abstract

We investigate oscillatory properties of perturbed half-linear Euler differential equation. We give an alternative proof (simpler and more straightforward) of the main result of [O. Došlý, H. Funková, Abstr. Appl. Anal. 2012, Art. ID 738472] and we prove the extended version of a conjecture formulated in [O. Došlý, J. Math. Anal. Appl. 323(2006), 426–440].

Keywords

• euler half-linear differential equation
• riemann-weber differential equation
• riccati technique
• modified riccati equation
• conditional oscillation