A remark on distribution of zeros of solutions of linear differential equations

Zheng, Jian Hua

doi:10.1090/S0002-9939-1995-1233976-1

A remark on distribution of zeros of solutions of linear differential equations
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by Jian Hua Zheng

Proc. Amer. Math. Soc. 123 (1995), 847-854

DOI: https://doi.org/10.1090/S0002-9939-1995-1233976-1

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Abstract:

The main purpose of this paper is to prove a sharp estimate of the order $\rho (w)$ of a transcendental solution w in the complex plane of an n th-order linear differential equation with polynomial coefficients in terms of the distribution of its Stokes rays, under the assumption that zero is not a Nevanlinna deficient value of w. If, in addition, there are only two Stokes rays and if all the solutions of the equation have order at most $\rho (w)$, then we can conclude that the coefficients of the equation are all constants.

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Theory of meromorphic and entire functions