MATHEMATICA BOHEMICA, Vol. 133, No. 2, pp. 187-195 (2008)

A remark on power comparison theorem for half-linear differential equations

Gabriella Bognar, Ondrej Dosly

Gabriella Bognar, Department of Mathematics, University of Miskolc, H-3514 Miskolc-Egytemvaros, Hungary, e-mail: matvbg@gold.uni-miskolc.hu; Ondrej Dosly, Department of Mathematics and Statistics, Masaryk University, Janackovo nam. 2a, CZ-602 00 Brno, Czech Republic, e-mail: dosly@math.muni.cz

Abstract: We consider the half-linear second order differential equation which is viewed as a perturbation of the so-called Riemann-Weber half-linear differential equation. We present a comparison theorem with respect to the power of the half-linearity in the equation under consideration. Our research is motivated by the recent results published by J. Sugie, N. Yamaoka, Acta Math. Hungar. 111 (2006), 165-179.

Keywords: Riemann-Weber half-linear equation, Riccati technique, power comparison theorem, perturbation principle, principal solution

Classification (MSC2000): 34C10

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