Some remarks on comparison functions

Volume 96 / 2009

Antoni Augustynowicz Annales Polonici Mathematici 96 (2009), 97-106 MSC: 34A12, 34A40. DOI: 10.4064/ap96-2-1


We answer some questions concerning Perron and Kamke comparison functions satisfying the Carathéodory condition. In particular, we show that a Perron function multiplied by a constant may not be a Perron function, and that not every comparison function is bounded by a comparison function with separated variables. Moreover, we investigate when a sum of Perron functions is a Perron function. We also present a criterion for comparison functions with separated variables.


  • Antoni AugustynowiczInstitute of Mathematics
    University of Gda/nsk
    Wita Stwosza 57
    80-952 Gda/nsk, Poland

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