The [p,q]-Proximate Order And [p-q]-Proximate Type Of Entire Functions、Analytic Functions And Their Applications In Complex Linear Differential Equations

In this thesis,the author first investigates the[p,q]-proximate order of f1(z)+f2(z)when f1(z)and f1(z)are entire functions or analytic functions in the unit disc,and also studies the growth of solutions of second order complex linear differ-ential equations with coefficients having[p,q]-proximate order and[p,q]-proximate type by taking advantage of Nevanlinna theory and complex oscillation theory.The results that obtained enrich and improve some previous results in complex oscillation theory.The thesis is divided into three chapters.In chapter 1,the author introduces some basic definitions and notations about value distribution theory of meromorphic function.In chapter 2,the author studies the[p,q]-proximate order and[p,q]-proximate type of f1(z)+f2(z)when the[p,q]-proximate order and[p,q]-proximate type of entire functions or analytic functions of f1(z),f2(z)have the same limit,and the results that the author obtained improve some previous results.In chapter 3,the author applies the proximate order and proximate type of entire function or analytic function into complex linear differential equations and investigates the growth of solutions of second order linear differential equa-tions with coefficients having[p,q]-proximate order and[p,q]-proximate type,the results that obtained enrich and improve some previous results in complex oscil-lation theory.