Applications Of Value Distribution Theory In Complex Difference And Differential Equations

The theories of ordinary differential equations and difference equations in complex plane are two important subjects in complex analysis. Many achievements in these topics have been obtained. In this thesis, we mainly study complex differential equations and complex difference equations, and obtain some interesting results. This thesis is divided into four parts.In chapter 1, we will give some usual notations, definitions and basic results in value distribution theory and Wiman-Valiron theory.In chapter 2, we obtain some results of Malmquist type theorem in complex difference equations, which generalize the related results due to Ablowitz,Heittokangas and Laine et al..In chapter 3, we study the Malmquist type theorem in algebraic differential equations, and obtain some results, which generalize the related results due to Ishizaki et al..In chapter 4, we investigate the meromorphic solutions of a class of complex differential equations, and obtain some results, which improve and generalize the related results due to Li-Yang.