The Complex Osciallation Properties Of Solutions Of Second Order And Higher Order Linear Differential Equations

In this thesis, by using the definition of hyper-order of entire or meromorphic function, we investigate the complex oscillation properties of the solutions of sec-ond order and higher-order linear differential equations. It includes the following three chapters.In chapter 1, we introuduce the difinitions concerning hyper-order and hyper-exponent of convergence of zero sequence of meromorphic function. In chapter 2, we investigate the hyper-order of solutions of higher-order linear differential equations with entire coefficients of small growth. For this type of equations, we obtain precise estimate of hyper-order of solutions of higher-order linear differential equations when one of the coefficients is dominating to the properties of the solutions. We improve some previous results.In chapter 3, we investigate the hyper-exponent of convergence of zero sequence of f(j)(z)—φ(z)(j = 0,1,2 ...) of second order linear differential equations. We obtain precise estimate of the hyper-order and the hyper-convergence exponent of the zero sequence of solutions of f(j)(z)—φ(z)(j = 0,1, 2 ? ...). We also improve some previous results.