On the Regularity of Solutions of Higher Order Differential Equations
YI Cai-feng, YANG Xiang-dong (Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China)
In this paper,we investigate the regularity of solutions of the equation f~((n))+a_(n-1)f~((n-1))+…+a_1f ′+a_0f=F, where coefficients a_i are polynomials,and F is a super entire function.It is proved that if F is regular and satisfies (σ(F)≥1+(max)1≤i≤ndega_(n-i)/i,)then every solution is regular. In addition,we have also considered the speaical case when coefficients are rational functions and got similiar results.
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