On the growth of solutions of some higher order linear differential equations

被引：1

作者：

El Farissi, Abdallah ^{[1
]}

Belaidi, Benharrat ^{[1
]}

机构：

[1] Univ Mostaganem UMAB, Lab Pure & Appl Math, Dept Math, Mostaganem, Algeria

来源：

APPLICATIONS OF MATHEMATICS | 2012年 / 57卷 / 04期

关键词：

linear differential equations; entire solutions; order of growth; exponent of convergence of zeros; exponent of convergence of distinct zeros;

D O I：

10.1007/s10492-012-0022-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f((k)) + A(k-1)f((k-1)) + ... + A(2)f '' + (D-1(z) + A(1)(z)e(az))f ' + (D-0(z) + A(0)(z)e(bz))f = F (k >= 2), where a, b are complex constants that satisfy ab(a - b) not equal 0 and A(j)(z) (j = 0, 1,..., k - 1), D-j(z) (j = 0, 1), F(z) are entire functions with max{rho(A(j)) (j = 0, 1, ..., k - 1), rho(D-j) (j = 0, 1)} < 1. We also investigate the relationship between small functions and the solutions of the above equation.

引用

页码：377 / 390

页数：14

共 18 条

[11]

Hayman W. K., 1964, Meromorphic functions

[12]

Jank G., 1985, EINFUHRUNG THEORIE G

[13]

Langley J. K., 1986, KODAI MATH J, V9, P430, DOI DOI 10.2996/kmj/1138037272

[14]

Markushevich A. I., 1965, Theory of functions of a complex variable, VII

[15]

Ozawa M., 1980, Kodai Math. J., V3, P295

[16] Growth of solutions of second order linear differential equations [J].

Wang, Jun ;

Laine, Ilpo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (01) :39-51

[17]

Xu HY, 2009, ELECTRON J QUAL THEO, P1

[18]

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