Study On The Growth Of Solutions Of Several Kinds Of Complex Differential Equations

This paper mainly by using the theory and method of Nevanlinna ofmeromorphic function to research a series of problems in the growth of solutions,thecomplex shocks and the value distribution of differential equations and so on. Thispaper organized five parts as follows:In chapter 1, in the research field we briefly introduces the development, theresearch background,basic knowledge of Nevanlinna value distribution theory andgives some related definitions and symbols.In chapter 2, Previous researched the growth of solutions of linear differentialequations,when0A(z) is a analytic function in unit circle1A(z),L1()kA z-is a notallowed analytic function in unit circle,But the chapter mainly researchedwhen0A(z),1A(z),L1()kA z-is a analytic function in unit circle,the growth ofsolutions of homogeneous linear differential equations()( 1)( 2) ’and inhomogeneous linear differential equations()( 1)( 2) ’In chapter 3, Previous researched the value distribution of()(( ))nf z +a f ￠z.Thechapter mainly researched the value distribution of the transcendental meromorphicfunction()(())nf ￠z +a f ￠z.n 32,n?z,a is non-zero finite complex numbers,b isnon-zero complex and f(z)is transcendental meromorphic function on the complexplane in this.In chapter 4, Previous researched the meromorphic solutions of differentialequation ( of complex shocks and get it’sconvergence index is infinite.On the basis of it,it for the conditions to be modified toresearched the differential equation ( of themeromorphic solutions of of complex shocks and get it’s convergence index in thedifferent zero.In chapter 5, Previous researched allow the solution of differential equationswhen the condition is {} { }1 1 11 2 2 22 max p,q 32l,max p,q 32l. This chapter relax theconditions get the meromorphic solutions of feasible,whe the condition is{ }1 1 11 max p,q 3l, { }2 2 22 max p,q 3l...