Some algebraic differential equations with few meromorphic solutions
Complex Variables
2014-01-14 v1
Abstract
A special class of autonomous algebraic differential equations is studied. No equations in the class have any entire transcendental solutions. In a sense, for almost all equations in the class, transcendental meromorphic solutions can also be excluded. With substantially fewer exceptional equations, transcendental solutions are either elliptic or of the form f(z) = g(exp(cz)) with g rational and c constant.
Cite
@article{arxiv.1401.2789,
title = {Some algebraic differential equations with few meromorphic solutions},
author = {P. X. Gallagher},
journal= {arXiv preprint arXiv:1401.2789},
year = {2014}
}