系数是周期 $ {2\pi}$i 的二阶复微分方程

Abstract

Abstract:

This paper mainly learned classic book `Nevanlinna theory and complex differential equations' due to Laine and considered the second order complex differential equation $f ''(z) + A (z) f(z)=0, \lambda(f)<\infty$ with coefficient $A (z) $ whose period is $2 \pi{\rm i}$. It found a possible error in the original proof and gave its partial correction, and also it gave a slightly weaker conclusion than its possibly controversial result in the original literature.

Key words: Complex differential equation, Nevanlinna theory, Entire function, Exponent of convergence for zero-sequence

CLC Number:

O174.52

Zhang Jie,Zhao Donghai. On Second Order Complex Differential Equations with Coefficients of Period $ {2\pi{\rm i}}$[J].Acta mathematica scientia,Series A, 2023, 43(5): 1382-1390.

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References 8

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On Second Order Complex Differential Equations with Coefficients of Period $ {2\pi{\rm i}}$

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