Value Distribution Of Meromorphic Solutions Of Complex Linear Differential Equations And Q-Shift Difference-Differential Polynomials

In this thesis, we mainly use Nevanlinna value distribution theory to investigate the growth and value distribution of meromorphic solutions of some kinds of complex linear differential equations in the complex plane and in the unit disc respectively. And we also investigate the value distribution of some kind of q-shift difference-differential polynomials. We obtain some results, which generalize and improve previous results. We divide this thesis into four chapters.In Chapter 1, we briefly introduce the development of the theory of value distri-bution of complex linear differential equations and the theory of complex differences and difference equations. We also introduce main content of this thesis and some basic definitions.In Chapter 2, we investigate the [p, g]-order, the [p, g]-lower order, the [p, q]-convergence exponent and the [p, g]-lower convergence exponent of the sequence of small function value points of meromorphic solutions of higher homogeneous and non-homogenous linear differential equations in the complex plane with some dom-inating coefficient being Lacunary gap series.In Chapter 3, we investigate the iterated convergence exponent and the iter-ated lower convergence exponent of the sequence of small function value points of differential polynomials, generated by meromorphic solutions of homogeneous and non-homogenous linear differential equations with meromorphic coefficients in the unit disc.In Chapter 4, we investigate the value distribution of some kind of g-shift difference-differential polynomials of entire functions with positive and finite order.