二阶线性微分方程解的零点与增长

Pub Date : 2018-09-12 DOI:10.4134/CKMS.C180494

Manisha Saini, Sanjay Kumar

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引用次数: 11

摘要

对于二阶线性微分方程$f' + a (z)f'+B(z)f=0$，当$ a (z)$和$B(z)$是在一定限制下的超越整函数时，我们证明了所有非平凡解都是无限阶的。此外，我们还证明了这些解有无限个零。同时，我们将这些结果推广到高阶线性微分方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ON ZEROS AND GROWTH OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restriction, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions have infinite number of zeros. Also, we have extended these results to higher order linear differential equations.

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