Transcendental Meromorphic Solutions Of Complex Differential Equations And Complex Difference Equations

The problems of the existence of transcendental meromorphic solutions of complexdifferential equation, complex difference equation and system of complex functional equationsare investigated by Nevanlinna theory of the value distribution of meromorphic functions andthe theory of differential equation. This taper is divided into four chapters:In chapter one, we describe the elementary knowledge of the theory of Nevanlinna’s valuedistribution, including related concepts and results, Poisson-Jensen formula, and fundamentaltheorems.In chapter two, using the Nevanlinna value distribution theory of meromorphic function andsome results of differential equation, investigate the problems of the existence oftranscendental meromorphic solutions of complex differential equation, improve someprevious results.In chapter three, the problems of the existence of transcendental meromorphic solutionsof complex difference equation are investigated by Nevanlinna theory of the value distributionof meromorphic functions and some results of difference equation, and some results ofreference are improved.In chapter four, using the Nevanlinna theory of the value distribution of meromorphicfunctions, we obtain main result on the meromorphic solutions of system of complex functionalequations becomes rational solutions, and extend some results concerning functional equationsto the systems of functional equations.