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.