On the growth of solutions of algebraic differential equations

Bank, Steven B.

doi:10.1090/S0002-9947-1978-0486718-6

On the growth of solutions of algebraic differential equations
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by Steven B. Bank

Trans. Amer. Math. Soc. 240 (1978), 195-212

DOI: https://doi.org/10.1090/S0002-9947-1978-0486718-6

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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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