The Growth of Solutions of Some Higher Order Linear Differential Equation

In this paper,the growth of solutions of some general homogeneous and non- homogeneous higher order linear differential equation is investigated.It is proved that under some conditions for entire functions F,A_j,D_j and polynomials P_j(z)with degree s≥1(j= 0,1,…,k-1),the equation(where k≥2)f~(k)+(A_(k_1)(z)e~(P~(k-1)(z))+D_(k-1)(z))f~(k-1)+…+ (A_0(z)eP_(0(z))+D_0(z))f=F satisfy the properties:when F≡0,all non-zero solutions are of infinite order;when F■0,at most one exceptional solution f_0 with finite order,all other solutions satisfy■(f)=λ(f)=σ(f)=∞andσ2(f)≤max{s,σ(F)}.These results generalize those of M.Frei,M.Ozawa,G.Gundersen,J.K.Langley,Chen Z.X.,Li C.H..