On the growth of solutions of algebraic differential equations-Reference-Cited by-同舟云学术

On the growth of solutions of algebraic differential equations

Published:1978 Issue:0 Volume:240 Page:195-212
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Bank Steven B.

Abstract

In this paper we determine estimates for the growth of both real-valued and complex-valued solutions of algebraic differential equations on an interval ( x 0 , + ∞ ) ({x_0}, + \infty ) . One of the main results of the paper (Theorem 3) confirms E. Borel’s conjecture on the growth of real-valued solutions for a broad class of solutions of second-order algebraic differential equations. The conjecture had previously been shown to be false for third-order equations.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1978-240-00/S0002-9947-1978-0486718-6/S0002-9947-1978-0486718-6.pdf

Reference25 articles.

1. On majorants for solutions of algebraic differential equations in regions of the complex plane;Bank, Steven;Pacific J. Math.,1969

2. On analytic and meromorphic functions satisfying 𝑛^{𝑡ℎ} order algebraic differential equations in regions of the plane;Bank, Steven;J. Reine Angew. Math.,1972

3. A general theorem concerning the growth of solutions of first-order algebraic differential equations;Bank, Steven B.;Compositio Math.,1972

4. On solutions of algebraic differential equations whose coefficients are analytic functions in the unit disk;Bank, Steven B.;Ann. Mat. Pura Appl. (4),1972

5. On determining the growth of meromorphic solutions of algebraic differential equations having arbitrary entire coefficients;Bank, Steven B.;Nagoya Math. J.,1973

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1. ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS;Acta Mathematica Scientia;2002-10

2. On Meromorphic Solutions of Some Algebraic Partial Differential Equations onCn;Journal of Mathematical Analysis and Applications;1997-10

3. Steven barry bank 1939–1994;Complex Variables, Theory and Application: An International Journal;1997-09

4. Bibliography;Nevanlinna Theory and Complex Differential Equations;1993-01-31

5. On the growth of real solutions of second-order algebraic differential equations;Journal of Mathematical Analysis and Applications;1984-04