The Growth Of The Solutions Of A Certain Type Of Differential Equations

In this thesis,suppose σ(Aj)=n(n is a positive integer),the Aj are of completely regular growth,hAj(θ)=cjhA0(θ),j=1,…,k-1,where cj>1(j=1,…,k-1)are distinct numbers.We prove the solutions of the equation f(k)+Ak-1(z)f(k-1)+…+ A0(z)f=0 have infinite growth order.Moreover,for the equation f(k)+Ak-1(z)f(k-1)+ …+A0(x)f=F,where F(z)is an entire function,we get two conclusion:(1)the equation above have at most one exceptional solution f0 with finite order,al-1 other solutions satisfy λ(f)=λ(f)=σ(f)=∞ and λ2(f)=λ2(f)=σ2(f)≤ max{n,σ(F)}；(2)if there exists an f0 with finite order,then σ(f0)≤max{n,λ(f0),σ(F)}.