The Growth Of Solutions Of Complex Differential Equations

In this paper,we study the growth of solutions of the following three kinds of differential equations by using the theory and method of Nevanlinna distribution.Firstly,the following two order linear differential equation:in the limit of A(z)is to satisfy the finite value of meromorphic functions with finite values,and the other is to satisfy the whole function of the Denjoy conjecture in the case of B(z)y we obtain that every nonzero solution of the equation(1)is infinite.Secondly,the higher order linear differential equations:andFor the equation(2)where the coefficients are meromorphic functions,the limit of a certain As:As satisfies a finite genus,in the case of σ(As)≠σ(A0),b=max{σ(Aj)(j≠0,s),λ(1/A0)}<μ(A0)≤σ(A0)≤1/2 and φ(z)(≠0)meromorphic function with finite order,we obtain a nonzero meromorphic solution of the equa-tion(2)is satisfiedFor the equation(3)where the coefficients and the Fare meromorphic functions,the limit of a certain number of As satisfies:and in the case of the solution of the equation(3)is obtained for each meromorphic solution ofσ(f)=∞.For a finite number of nonzero meromorphic functions φ(z),(Whereφ(z)is a small function of f(z)),then every nonzero meromorphic solution of equation(3)is satisfied:λ(f-φ)=λ(f)=σ(f)=∞Finally,the research about complex domain beyond the value distribution theory of meromorphic function difference problem and holomorphic functions an inequality about the characteristic function.