The Logarithmic Proximate Order And Logarithmic Proximate Type Of Entire Functions?Analytic Functions And Their Applications In Complex Linear Differential Equations

In this paper,the author first investigates the logarithmic proximate order and logarithmic proximate type 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 differential equations with coefficients having logarithmic proximate order by taking advantage of Nevenlinna theory and complex oscillation theory.The thesis is divided into three chapters.In chapter 1,the author introduces some basic definitions and notations about,meromorphic function and value distribution theory.In chapter 2,the author studies the logarithmic proximate order and logarith-mic proximate type of f1(z)+f2(z)of entire functions or analytic functions in the unit disc,when the logarithmic proximate order and the logarithmic proximate type of f1(z)+f2(z)have the same limit or different limit.The results obtained enriches obtained and improves some previous results.In chapter 3,the author applies the logarithmic proximate order and loga-rithmic proximate type of entire function or analytic function into complex linear differential equations and investigate the growth of solutions of second order lin-ear differential equations with coefficients having logarithmic proximate order,the results that obtained enrich and improve some previous results in complex oscil-lation theory.