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一类高阶微分方程解的增长性
  • ISSN号：1006-8074
  • 期刊名称：数学理论与应用
  • 时间：2013.3.3
  • 页码：19-22
  • 分类：O174.52[理学—数学;理学—基础数学]
  • 作者机构：[1]江西师范大学数学与信息科学学院,江西南昌330022
  • 相关基金：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
  • 相关项目：变指数函数空间理论中的一些问题
作者： 田逢池,|黄斌|
关键词： 微分方程, 增长级, 零点收敛指数, 超级, differential equation； order of growth； exponent of convergence； hyper-order
中文摘要：

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.

英文摘要：

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.

同期刊论文项目
函数的唯一性问题和非齐次线性微分方程解的性质
期刊论文 31
变指数函数空间理论中的一些问题
期刊论文 32 著作 1
亚纯系数微分方程与单位圆内的微分方程解的性质
期刊论文 47 会议论文 3 获奖 4
复域差分, 差分方程和微分方程的研究
期刊论文 126 著作 1
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期刊信息
  • 《数学理论与应用》
  • 主管单位:中南大学
  • 主办单位:湖南省数学学会
  • 主编：黄云清
  • 地址：湖南省长沙市岳麓区中南大学本部
  • 邮编：410075
  • 邮箱：hyprob@csu.edu.cn
  • 电话：0731-82655243
  • 国际标准刊号：ISSN：1006-8074
  • 国内统一刊号：ISSN：43-1334/O1
  • 邮发代号:42-187
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘
  • 被引量:2392