## Hille-Wintner type comparison criteria for half-linear
second order differential equations

*O. Dosly, Z. Patikova*

**Address****.**

Department of Mathematics, Masaryk University, Janackovo
nam. 2a, 662 95 Brno, Czech
Republic

Department of
Mathematics, Tomas Bata University, Nad Stranemi
4511, 760 05 Zlin, Czech Republic

**E-mail: **dosly@math.muni.cz, patikova@ft.utb.cz

**Abstract****.**

We establish Hille-Wintner type comparison criteria for the half-linear second order
differential equation $$ \left(r(t)\Phi(x')\right)'+c(t)\Phi(x)=0,\quad \Phi(x)=|x|^{p-2}x\,,\
p>1\,,
%\leqno{(*)} $$ where
this equation is viewed as a perturbation of another equation of the same
form.

**AMSclassification**.
34C10.

**Keywords**. Half-linear differential equation, Hille-Wintner comparison criterion, Riccati equation, principal solution.