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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the growth of solutions of algebraic differential equations


Author: Steven B. Bank
Journal: Trans. Amer. Math. Soc. 240 (1978), 195-212
MSC: Primary 34A20
MathSciNet review: 0486718
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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}, + \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.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0486718-6
Keywords: Algebraic differential equations, growth of solutions
Article copyright: © Copyright 1978 American Mathematical Society