On the Zero Distribution of Solutions of Second Order Linear Differential Equations in the Complex Domain

From NZJM

Jump to: navigation, search

New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 9-16


Jianren Long

School of Mathematics and Computer Science,

Guizhou Normal University,

Guiyang, 550001, P. R. China

mailto:longjianren2004@163.com

Pengcheng Wu

School of Mathematics and Computer Science,

Guizhou Normal University,

Guiyang, 550001, P. R. China

mailto:wupc@gznu.edu.en

Xiubi Wu

School of Mathematics and Computer Science,

Guizhou Normal University,

Guiyang, 550001, P. R. China

mailto:basicmath@163.com


Abstract Let f(z)\not \equiv 0 be a solution of f'' + P(z)f = 0, where P(z) is a polynomial. Then the set of accumulation lines of zero-sequence is a subset of the Borel directions of f(z). Let f1 and f2 be two linearly independent solutions of f'' + P(z)f = 0, where P(z) is a polynomial of degree n and set E = f1f2. Then, for every accumulation line \arg z =\theta of zero-sequence of E, there is another accumulation line \arg z =\phi of zero-sequence of E such that |\phi-\theta|=\frac{2\pi}{n+2}.

Keywords Differential equation, accumulation line of zero-sequence, exponent of convergence of zero-sequence, angular distribution.

Classification (MSC2000) 34M10; 30D35.

Full text

Full paper

Personal tools