高阶线性微分方程解的完全正规增长性

Abstract

Abstract:

In this paper, the existence of completely regular growth solutions of higher order linear differential equations is studied, where its dominant coefficient is an exponential polynomial. By using the Nevanlinna characteristic of exponential polynomials, some conditions which guarantee the non-existence of such solutions are obtained. At the same time, for the higher order linear differential equation with exponential polynomial solutions, the relationship between the expression of its solutions and dominant coefficient is given.

Key words: Linear differential equation, Completely regular growth, Exponential polynomial, Entire function

CLC Number:

O174.52

Chen Li,Liu Huifang. The Completely Regular Growth of Solutions of Higher Order Linear Differential Equations[J].Acta mathematica scientia,Series A, 2023, 43(3): 733-742.

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References 18

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The Completely Regular Growth of Solutions of Higher Order Linear Differential Equations

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