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... (inherent in the model) is shown to be a transcendental number.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-4,
author = {Peter Kahlig},
title = {A model of competition},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {293-303},
zbl = {1258.39013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-4}
}
Peter Kahlig. A model of competition. Applicationes Mathematicae, Tome 39 (2012) pp. 293-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-3-4/