The Complex Oscillation Property Of Solutions Of Some Linear Differential Equations With Entire Coefficients

In this thesis, we mainly use the related theory of entire functions and the Nevanlinna fundamental theory of meromorphic functions to discuss the complex oscillation properties of solutions of some linear differential equations with entire coefficients. It consists of four chapters.In chapter one, as the pre-knowledge of the whole paper, we briefly introduce the related knowledge of entire functions and the Nevanlinna fundamental theory of meromorphic functions.In chapter two, we investigate the relations between solutions of second order linear differential equations and their 1th and 2th derivatives with the small growth functions by using the related theory of entire functions and the Nevanlinna fundamental theory of meromorphic functions.In chapter three, we investigate the growth of solutions of some higher order linear differential equations by using the related theory of entire functions and the Nevanlinna fundamental theory of meromorphic functions. When supposing()sA z be a solution of the differential equation f ? ?P(z) f ?0, where P(z) is a polynomial with deg P(z) ?n and giving some conditions on other coefficients of the higher order linear differential equation()( 1)1 1 00 k k kf A f A f A f??? ???? ? ?, then every nonzero solution of the differential equation satisfies ?( f) ? ?.In chapter four, we investigate the measure in an angle and the Borel direction of infinite order solutions of a class higher order complex linear differential equations by using the related theory of entire functions and the Nevanlinna fundamental theory of meromorphic functions when guaranteeing that every nonzero solution of the complex linear differential equation()( 1)1 1 00 k k kf A f A f A f??? ???? ? ? has infinite order. Firstly a general result is obtained, then by combining with the discussion about the deficient value theory and the Borel directions of entire functions, the results are further improved.