摘要
研究了高阶线性齐次微分方程f(k)+Ak-1(z)Pk-1(ez)f'+…+A1(z)P1(ez)f'+A0(z)P0(ez)f=0解的增长性,其中Aj(z)■0(j=0,1,…,k-1)是整函数,Pj(ez)(j=0,1,…,k-1)是ez的非常数多项式,它们的常数项都为零,且次数不相等。证明了该微分方程的每一个非零解有无穷级。
The growth of solutions of higher order homogeneous linear differential equationf(1)+A k-1(e2)f1+……+A1(z)P1(e2)f+A0(z)P0(ez)f=0 is investigated, whereA,(z)≠O(j=0,1,…,k-1)are entire functions,P1(ez)(J=0,1,…,k-1)are nonconstant polynomials of e~ without constant term, and deg P(z) is not equal to deg Q(z) . It is showed that the order of growth of each nonzero solution of the above equations is infinite.
出处
《中山大学学报(自然科学版)》
CAS
CSCD
北大核心
2013年第1期51-54,共4页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
贵州省科学技术基金资助项目(2012GZ10526
2010GZ43286)
贵州省毕节地区科研基金资助项目([2011]02)
关键词
线性微分方程
整函数
增长级
linear differential equations
entire function
order of growth