A model of competition

Volume 39 / 2012

Peter Kahlig Applicationes Mathematicae 39 (2012), 293-303 MSC: Primary 39B12, 39B22; Secondary 34A05. DOI: 10.4064/am39-3-4

Abstract

A competition model is described by a nonlinear first-order differential equation (of Riccati type). Its solution is then used to construct a functional equation in two variables (admitting essentially the same solution) and several iterative functional equations; their continuous solutions are presented in various forms (closed form, power series, integral representation, asymptotic expansion, continued fraction). A constant $C = 0.917\ldots$ (inherent in the model) is shown to be a transcendental number.

Authors

  • Peter KahligA-1120 Vienna, Austria
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