| 一类高阶微分方程解的增长性 |
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| 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(4):335-338,354. |
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| 作者姓名： | 冯斌 刘慧芳* 李延玲 |
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| 作者单位： | 江西师范大学数学与信息科学学院, 江西 南昌 330022 |
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| 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 |
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| 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.
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| 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 |
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| 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(4):335-338,354. |
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| Authors: | FENG Bin LIU Hui-fang LI Yan-ling |
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| Institution: | (College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China) |
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| 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. |
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| Keywords: | differential equation order of growth exponent of convergence hyper-order |
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