摘要
研究了齐次方程 f(4 ) +kf′ +ezf =0的复振荡 ,其中k∈C为常数 .得到该方程有非平凡解 f ,其零点的密指量等价于o(er)时的充要条件是k =(n +3 2 ) 3 / 4 3 ,其中n是正整数 ,满足 (n +1)× (n +1)阶行列式的某些条件 ,进一步得到非平凡解 f的表达式 .
In this paper,the complex oscillation of the different ia l equation f- (4)+kf′+e-zf=0,where k i s a complex constant has been investigated.The above equation admits a non-triv ial solution f such that log-+N(r,1/f)=o(r) (as r→∞) if and only if k=(n+3/2)-3/4-3,where n is a positive integer,has been proved,and satisfied a certain (n+1)×(n+1 ) determinant condition.Moreover,the representation for such solution has been obtained.
出处
《江西师范大学学报（自然科学版）》
CAS
2000年第2期101-106,共6页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目!(1976 10 0 2 )
关键词
线性微分方程
非平凡解
四阶
解
复振荡
linear differential equation
non-trivial solution
zero exponent of convergence
