The Complex Oscillation Properties Of Solutions Of Second Order And Higher Order Linear Differential Equations With Coefficients Of Finite Iterated Order

In this thesis, we investigate the complex oscillation properties of solutions ofsecond order and higher order linear di?erential equations with coe?cients of finiteiterated order. The thesis is divided into three chapters.In Chapter 1, we give a brief introduction of history on development of thisreach field, and introduce the definitions about iterated order and iterated exponentof convergence of zero sequence of meromorphic function.In Chapter 2, we study the growth of solutions of complex higher order lineardi?erential equations with entire or meromorphic coe?cients of finite iterated orderand we obtain some results which improve and extend some previous results in [3,4, 9, 10].In Chapter 3, we investigate the iterated exponent of convergence of zero se-quence of f^(j)(z)(?)(z)(j = 0,1,2,···), where f is a solution of second order lineardi?erential equation, (?)(z)≡0 is an entire function satisfyingσ_p+1(?) <σ_p+1(f) ori(?) < i(f)(p∈N). We obtain some results which improve and generalize someprevious results in [3, 6] and which provide us a method to investigate the iteratedexponent of convergence of zero sequence of f^(j)(z)(?)(z)(j= 0,1,2,···).