Hille-Wintner type comparison criteria for half-linear second order differential equations. (English) Zbl 1164.34386

Došlý, Ondřej; Pátíková, Zuzana

Arch. Math., Brno 42, No. 2, 185-194 (2006).

The authors are concerned with a half-linear second order differential equation \[ \big (r(t)\Phi (x')\big )'+c(t)\Phi (x)=0, \tag{1} \] where \(\Phi (x)=| x| ^{p-2}x\), \(p>1\). They give Hille-Wintner type comparison criteria for nonoscillation and oscillation of equation (1) which is considered as a perturbation of another equation of the same form. The method of the proof is based on the relationship between nonoscillation of equation (1) and solvability of the associated Riccati differential equation on some interval \([T,\infty )\).

Reviewer: Josef Kalas (Brno)

MSC:

34C10

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

Keywords:

half-linear differential equation; Hille-Wintner comparison criterion; Riccati equation