## Abstract and Applied Analysis

### The Hyperorder of Solutions of Second-Order Linear Differential Equations

Guowei Zhang

#### Abstract

We prove that the hyperorder of every nontrivial solution of homogenous linear differential equations of type $f\mathrm{\prime }\mathrm{\prime }+{A}_{\mathrm{1}}\left(z\right){e}^{az}f\mathrm{\prime }+{A}_{\mathrm{0}}\left(z\right){e}^{bz}f=\mathrm{0}$ and nonhomogeneous equation of type $f\mathrm{\prime }\mathrm{\prime }+{A}_{\mathrm{1}}\left(z\right){e}^{az}f\mathrm{\prime }+{A}_{\mathrm{0}}\left(z\right){e}^{bz}f=H\left(z\right)$ is one, where ${A}_{\mathrm{0}},{A}_{\mathrm{1}},H\left(z\right)$ are entire functions of order less than one, improving the previous results of Chen, Wang, and Laine.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 626898, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512019

Digital Object Identifier
doi:10.1155/2013/626898

Mathematical Reviews number (MathSciNet)
MR3095357

Zentralblatt MATH identifier
07095183

#### Citation

Zhang, Guowei. The Hyperorder of Solutions of Second-Order Linear Differential Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 626898, 7 pages. doi:10.1155/2013/626898. https://projecteuclid.org/euclid.aaa/1393512019

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