关于n-阶线性周期微分方程的次正规解

On Subnormal Solutions of n-Order Linear Periodic Differential Equations

研究了n-阶周期系数齐次线性微分方程f(n)+[Pn-1(ez)+Qn-1(e-z)]f(n+1)+…+[P0(ez)+Q0(e-z)]f=0及其对应的非齐次线性微分方程次正规解的存在性和解的增长性,其中Pj(z),Qj(z)(j=1,…,n-1)为多项式,在假设degP0>degPj或者degQ0>degQj的条件下,证明了齐次方程没有非平凡的次正规解,且它的每个非平凡解的超级满足σ2(f)=1.

In this paper, we investigated the existence of subnormal solution and the growth properties of solutions for n- order periodic coefficient homogeneous linear differential equations f^（n）＋[Pn-1（e^z）＋Qn-1（e^-z）]f^（n＋1）＋…＋[Po（e^z）＋Q0（e^-z）]f=0（where Pj（z）,Qj（z）（j=1,…,n-1） are polynomal） and its corresponding non-homogeneous equation, we proved the non-existence of subnormal solutions of homogeneous differential equations and the hype order of non-trivial solution satisfied σ2（f） = 1 ifdegP0 〉 degPj or degQ0 〉 degQj .