The Complex Oscialliation Properties Of Higher Order Linear Differential Equations With Entire Coefficients Of "p, Q" Order

In this thesis, we investigate the complex oscillation properties of the solutions of some classes of linear differential equations with entire coefficients of [p, q] order by the value distribution theory of Nevanlinna and the methods of wiman-varilon. It contains three chapters. In chapter 1, we give a brief introduction of history on development of this research field, and introduce some preliminary knowledge, definitions and notations. In chapter 2, we investigate complex oscillation properties of the solutions of some classes of higher-order linear differential equations with entire coefficients of [p, q]-order, we make use of the definition of entire functions of [p, q] order to investigate the growth of solutions of a class of homogeneous and non-homogeneous higher order linear differential equations with entire ciefficients of [p, q] order. We obtain the precise estimate of the growth and the covergence exponent of the zero sequence of the solutions of the above equations when there is some coefficient being dominated to the other coefficients in these equation.In a word, we investigate the complex oscillation properties of the higher-order linear differential equations with the more general coefficients and obtain some results which improve previons results.