The Growth Of The Solutions Of Some Classes Of Linear Differential Equations

In this thesis,we investigate the complex oscillation properties of the solutions of some types of linear differential equations by applying the theories and methods of the complex analysis.At first,we investigate the growth of solutions of the equation f(k)+Ak-1(z)ePk-1(k-1) +…+A0(z)eP0 f=0,where Aj is a entire function,σ(Aj)≤σ(j=0,…,k-1),Pj is a polynomial,deg Pj=n(n≥1).We mainly extend,improve,or complement the existing results.Secondly,we investigate six propositions of the type of entire functions.In fact,we obtain some relations between the type of the entire function and the order of it.At last,we investigate the growth of solutions of the equation f(k)+(Ak-1ePk-1+ Dk-1)f(k-1)+…+(A0eP0+D0)f=0 where Aj(z),Dj(z)are entire functions,σ(Aj)< n,σ(Dj)