Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

Meromorphic Solutions of a Differential Equation with Polynomial Coefficients We give new estimates for the maximum number M of distinct meromorphic solutions and also for the maximum number L of linearly independent meromorphic solutions of the first order differential equation $$f^\prime = p_0+p_1f+...+p_nf^n,\ \ \ n\geq 3,$$ where each P k is a polynomial and P n ≢ 0. The estimate for M depends only on n and the number d of distinct zeros of P n, while the estimate for L depends only on d. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Meromorphic Solutions of a Differential Equation with Polynomial Coefficients

Loading next page...
 
/lp/springer-journals/meromorphic-solutions-of-a-differential-equation-with-polynomial-0E8e1zji5v
Publisher
Springer Journals
Copyright
Copyright © 2008 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321665
Publisher site
See Article on Publisher Site

Abstract

We give new estimates for the maximum number M of distinct meromorphic solutions and also for the maximum number L of linearly independent meromorphic solutions of the first order differential equation $$f^\prime = p_0+p_1f+...+p_nf^n,\ \ \ n\geq 3,$$ where each P k is a polynomial and P n ≢ 0. The estimate for M depends only on n and the number d of distinct zeros of P n, while the estimate for L depends only on d.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 27, 2007

References