On The Existence Of Solutions Of Certain Type Of Nonlinear Differential Equations

Nevanlinna Theory(refer to[1],[2],[3],[4])as one of the most perfect achievements in last century not only takes an important position in mathematics,but also inherits the great value in applications from function analysis.Nevanlinna Theory paves the path of research on value distribution of meromorphic functions, constructs characteristic function and overcomes the restriction of meaningless of maximum module function on meromorphic functions.Due to the broad correlation with other fields and mutual influence,both Nevanlinna Theory and others take big strides.The value distribution of module of function directly based on Nevanlinna Theory provides a new approach in research on differential equation.It gives a decent example for the angular value distribution theory and value distribution theory on p-adic field,n-dimentional complex Euclidian space,and even on general manifold.Moreover.Nevanlinna's value distribution theory of meromorphic functions has been used to study or tackle the growth,oscillation,solvability and existence of entire or meromorphic solutions of differential equations in complex domains.The first such applications were made,to the best of our knowledge,by Nevanlinna.who considered the differential equation f"+A(z)f=0 in the ease of a polynomial A(z). The first one who made systematie studies in the applications of Nevanlinna Theory into complex differential equations was H.Wittich beginning from 1942.This paper is concerned with the existence of entire solutions of certain type of nonlinear differential equations.In Chapter 1.we describe the basic Nevanlinna Theory briefly.In Chaptet 2,we will give preliminaries,introduction and main results.