二阶线性微分方程解的正规性问题

The Regularity of Solutions of Second Order Differential Equations

研究了二阶线性微分方程f″+A1f′+A0f=F解的增长级的正规性问题,得到了如下结论:当Ai为有理函数且A1=P/R,A0=Q/R,其中P,Q,R为多项式,而F为超越亚纯函数时,方程的解是否正规,完全取决于F是否正规.我们还在假定系数a1(z)为具有有限个极点的超越亚纯函数的条件下,讨论了方程f″+a1f′=0以及f′+a1f=0的解的正规性问题.

In this paper,we have investigated the regularity of solutions of f ″+A1f ′+A0f=F.It is proved that the regularity of the solutions of this kind of equations depends totally on the regularity of F when A1 and A0 are both rational.In addition,we discuss the special cases:f ″+a1f ′=0 and f ″+a1f=0.