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一类高阶微分方程解的增长性
引用本文:冯斌,刘慧芳*,李延玲. 一类高阶微分方程解的增长性[J]. 江西师范大学学报(自然科学版), 2012, 0(4): 335-338,354
作者姓名:冯斌  刘慧芳*  李延玲
作者单位:江西师范大学数学与信息科学学院, 江西 南昌 330022
基金项目:国家青年基金(11201195);国家自然科学基金(11171119);江西省教育厅科技(GJJ12179)资助项目
摘    要:研究了微分方程f~(k)+A_(k-1)f~(k-1)+…A_2f″+A_1e~(az~n)f′+A_0e~(bz~n)f=F解的增长性,其中A0(z)、A1(z)、F(z)是级小于n的整函数,A j(z)(j=2,3,…,k 1)是次数不超过m的多项式,a、b为非零复常数.证明了该方程的所有解f(z)满足(f)=λ(f)=σ(f)=∞,2(f)=λ2(f)=σ2(f)=n,至多除去2个例外复数b.

关 键 词:微分方程  增长级  零点收敛指数  超级

On the Growth for Solutions of a Certain Higher Order Differential Equation
FENG Bin,LIU Hui-fang,LI Yan-ling. On the Growth for Solutions of a Certain Higher Order Differential Equation[J]. Journal of Jiangxi Normal University (Natural Sciences Edition), 2012, 0(4): 335-338,354
Authors:FENG Bin  LIU Hui-fang  LI Yan-ling
Affiliation:(College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China)
Abstract:The growth for solutions of a differential equationfk+Ak-1fk-1+…A2f″+A1eaznf′+A0ebznf=F has been investigated,where A0(z),A1(z) and F(z)are entire functions with order less than n,Aj(z)(j=2,3,…,k-1) are polynomials with degree no more than m,a and b are nonzero complex numbers,then every solution f(z) of the above equation satisfies (f)=λ(f)=σ(f)=∞,2(f)=λ2(f)=σ2(f)=n,except at most two exceptional complex numbers b.
Keywords:differential equation  order of growth  exponent of convergence  hyper-order
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