On the relationship between the lower order of coefficients and the growth of solutions of differential equations

被引：21

作者：

Long, Jianren ^{[1
,2
]}

Heittokangas, Janne ^{[2
]}

Ye, Zhuan ^{[3
]}

机构：

[1] Guizhou Normal Univ, Sch Math Sci, Guiyang 550001, Peoples R China

[2] Univ Eastern Finland, Dept Math Phys, POB 111, Joensuu 80101, Finland

[3] Univ N Carolina, Dept Math & Stat, 601 South Coll Rd, Wilmington, NC 28403 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 444卷 / 01期

基金：

中国国家自然科学基金; 芬兰科学院;

关键词：

Asymptotic growth; Complex differential equation; Density; Growth of solutions; Hyper-order; Lower order; THEOREMS;

D O I：

10.1016/j.jmaa.2016.06.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some criteria for entire coefficients A(z) and B(z) are given in terms of the lower order forcing the solutions of f '' + A(z) f' + B(z)f = 0 to grow fast. In the literature similar criteria have been published in terms of the usual order. The case when the coefficient A(z) has an asymptotic growth T(r, A) similar to alpha log M(r, A), alpha is an element of (0,1), outside of an exceptional set is also discussed. Previously, Laine-Wu (2000) and Kim-Kwon (2001) have made use of this asymptotic growth in the case alpha = 1. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：153 / 166

页数：14

共 27 条

[1] [Anonymous], 1975, Potential theory in modern function theory
[2] BANK SB, 1972, COMPOS MATH, V25, P61
[3] BARRY PD, 1970, P LOND MATH SOC, V21, P334
[4] ON INTEGRAL FUNCTIONS HAVING PRESCRIBED ASYMPTOTIC GROWTH
CLUNIE, J
[J]. CANADIAN JOURNAL OF MATHEMATICS, 1965, 17 (03): : 396 - &
[5] EDREI A, 1969, T AM MATH SOC, V140, P309
[6] EDREI A, 1973, P LOND MATH SOC, V26, P435
[7] Goldberg A. A., 1970, TRANSL MATH MONOGR, V236
[8] GUNDERSEN GG, 1988, T AM MATH SOC, V305, P415
[9] GUNDERSON G, 1988, LONDON MATH SOC, V37, P88
[10] Heittokangas J., 2013, Fields Inst. Commun., V65, P43

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