Abstract and Applied Analysis

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients

Jianren Long, Chunhui Qiu, and Pengcheng Wu

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Abstract

We consider that the linear differential equations f ( k ) + A k - 1 ( z ) f ( k - 1 ) + + A 1 ( z ) f + A 0 ( z ) f = 0 , where A j   ( j = 0,1 , , k - 1 ) , are entire functions. Assume that there exists l { 1,2 , , k - 1 } , such that A l is extremal for Yang's inequality; then we will give some conditions on other coefficients which can guarantee that every solution f ( 0 ) of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder of f if every solution f ( 0 ) of the equation is of infinite order.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 305710, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276900

Digital Object Identifier
doi:10.1155/2014/305710

Mathematical Reviews number (MathSciNet)
MR3198173

Zentralblatt MATH identifier
07022131

Citation

Long, Jianren; Qiu, Chunhui; Wu, Pengcheng. On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients. Abstr. Appl. Anal. 2014 (2014), Article ID 305710, 7 pages. doi:10.1155/2014/305710. https://projecteuclid.org/euclid.aaa/1412276900


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