The Growth And Distribution On Solutions Of Some Class Of Nonhomogeneous Linear Differential Equations

In this paper, we mainly use Nevanlinna value distribution theory and Wiman-Valiron theory to investigate the growth and distribution of solutions of some classof non-homogeneous linear diferential equations in complex domain. It consistsof three chapters.In chapter1, we briefly introduce the history of complex diferential equation,and also give some knowledge used in the following chapters.In chapter2, we investigate the properties of solutions of the second non-homogeneous linear diferential equationwhere A0(z), A1(z), F (z) are all entire functions with order less than n. We obtainsome conditions which guarantees that every non-trivial solution of such equationwill have infinite order. And we also investigate the properties of the fixed-pointsof solutions of such equation. Those results in this chapter extend some previousresults.In chapter3, we investigate the growth and the properties of zeros of solutionsof the higher non-homogeneous linear diferential equationwhere Aj(z)(j=2,···, k1) are polynomials, A0(z), A1(z), F (z)are all entirefunctions with order less than n. Under certain conditions, we obtain the preciseestimation of the order and the exponent of convergence of zeros of solutions ofthe above equation.