English

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.

Keywords

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}
}
R2 v1 2026-06-22T02:43:55.450Z