Oscillation and nonoscillation of perturbed half-linear Euler differential equations. (English) Zbl 1164.34012

Došlý, Ondřej; Řezníčková, Jana

Publ. Math. Debr. 71, No. 3-4, 479-488 (2007).

The authors derive new oscillation and nonoscillation criteria for the perturbed half-linear Euler differential equation \[ (\Phi(x'))' +\left[\frac{\gamma_p}{t^p} +c(t)\right]\Phi(x)=0, \] where \(\gamma_p:=\left(\frac{p-1}{p}\right)^p\), \(\Phi(x):=| x| ^{p-2}x\), and \(p>1\). These criteria are motivated by the conjectures which were proposed in earlier separate papers by the authors. The methods traditionally use the variational and Riccati techniques.

Reviewer: Roman Simon Hilscher (Brno)

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

Euler half-linear equation; perturbation principle; (non)principal solution; variational principle; Riccati technique