On a functional equation for Dido's problem
Abstract
By some geometrical considerations we formulate a functional equation which is related to the ancient isoperimetric problem of Dido. The continuous solution of this Dido functional equation depends on an arbitrary function. However, we show that in a class of functions of suitable asymptotic behavior at infinity, the Dido functional equation has a one-parameter family of "principal" solutions. Some applications are given.
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Institute of Meteorology and Geophysics, University of Vienna , Austria Austria
Instytut Matematyki, Wyższa Szkoła Pedagogiczna im. Tadeusza Kotarbińskiego w Zielonej Górze & Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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