The Order And Type Of Entire Functions And[p,q]-order Of The Solutions Of Complex Differential Equations

In this paper,we investigate the[p,q]-φ(r)order and[p,q]-φ(r)type of two meromorphic functions and analytic functions in the unit disc by using the Nevan-linna value distribution theory in the unit disc,and we also investigate the complex oscillation properties of the solutions of linear differential equations with analyt-ic functions with[p:q]-φ(r)order in the unit disc,we obtain some results which improve some previous results.In chapter 1,we introduce some basic definitions and notations of Nevanlinna value distribution theory in the unit disc,including the[p,q]order and[p,q]-φ(r)or-der of meromorphic functions and analytic functions,we also introduce the research background of our thesis.In chapter 2,we also study the[p,q]-φ(r)order,[p,g]-φ(r)type of f1 + f2,f1f2,wheref1,f2 are meromorphic functions or analytic functions of[p,q]-φ(r)order,and we also study the[p,q]-φ(r)order and[p.q]-φ(r)type of the derivative of a mero-morphic function or an analytic function in the unit disc.In chapter 3,we mainly investigate the complex oscillation properties of the solutions of linear differential equations with analytic funtions of[p,q]-φ(r)order in the unit disc,which mainly includes the growth and the zeros of the solutions.