On The Growth Of Solutions Of Linear Differential Eauations With Whose Coefficients Have A Deficient Value

In this paper, we investigated oscillation of solutions of linear differential equations with which coefficients have a deficient by using value distribution theory and method of Nevanlinna. There are three chapters in this paper.In chapter one, we first introduce the background of oscillation differential equations, then narrate some preliminary knowledge of Nevanlinna theory and some related definition.In chapter two, we mainly investigates the the nature of the solution of second order linear differential equation f"+A(z)f’+B(z)f=0. We proved that every nontrivial solution of equation has infinite growth and investigate the zero point of solution when it take small function under the condition that A (z) is a meromorphic function with a finite dificient value, B(z) satisfied the two kinds of conditions,In chapter three, we investigates the growth of higher order linear differential equations f(k)+Ak-1f(k-1)+…+A0f= 0 under the condition that Aj(j=0,1…,k-1)is a meromorphic function and there is a Aj (j∈e{1,…,k-1}) has a finite deficient value. We proved that the nonzero solution of equations has infinite growth successively by giving a different condition to A0. Lastly we discuss the super growth and secondly zero convergence index of the nonhomogeneous higher order linear equations.