The Properties Of Solutions And Solutions Space Of Differential Equations In The Complex Plane And The Unit Disc

In this paper, we investigated some properties of solution of some types of the linear differential equations by using the value distribution theory and methods of Nevanlinna. The article is divided into the following four chapters.In chapter 1, we give a brief introduction of the status of research on the theory of differential equation of complex oscillation, as well as the research background of this article, and lead into some related notation, definitions.In chapter 2, we investigated the properties of solutions of the second nonhomogeneous linear differential equation,we obtain estimate of solution and hyper-order of such equation, and we also investigate the properties of fixed-points of solution of such equation. Those results in this chapter extend some previous results.In chapter 3, we investigate the problem of solution of a class of second order linear differential equation are polynomials in z. When coefficients of the polynomial are transcendental entire function, the precise estimation of their hyper-order are obtained.In chapter 4, we investigate the property of the solutions of higher order nonhomogeneou linear differential equations in the unit disc. We obtain the space property of the solutions of the equation.