The Order Of Growth And The Exponent Of Convergence Of The Solutions Of Linear Differential Equations

In this thesis, we investigate the complex oscillation properties of the solution of linear differential equations by applying with the theories and methods of the complex analysis. It includes following four sections.In section 1, we give a belief introduction of the development history of this research field and introduce the concerning definitions.In section 2, we discuss the problem of the relationship between the solution of homogeneous linear differential equation and small function and obtain some precise estimates for their hyper order and their hyper exponent of convergence of the distinct zeroes.In section 3, we investigate hyper order of solutions of second order linear differential equations with meromorphic coefficients with iterated order, we obtain precise estimate of hyper order under certain conditiions.In section 4 , we investigate the growth of certain second order linear differential equation f" + A1(z)eaz f' + A0(z)ebzf = 0,prove that all meromorphic solutions of above equations with meromorphic coefficients have infinite order. We also improve the results obtained by some authors.