Studies On The Crossing Problems Of Value Sharing And Malmquist Systems

In the 1920 s,R.Nevanlinna established the famous value distribution theory of meromorphic functions over the complex field which is also called Nevanlinna theory,Up to now,it is still an important branch of complex analysis.Based on the theory of value distribution and uniqueness of meromorphic function,this paper mainly studies the uniqueness problem of value cross-sharing and the solutions of some crossing differential or difference Malmquist equations by relying on the classical theorem of sharing common values in the uniqueness theory of meromorphic functions and the existence theorem of meromorphic solutions of algebraic differential or difference equations.In chapter 1,we mainly introduce the research background and main research issues of this paper.In chapter 2,we mainly introduce some basic concepts and some relevant lemmas which will be used in this paper.In chapter 3,we mainly study the uniqueness problem of value cross-sharing of meromorphic functions.In chapter 4,we mainly study the problem of solutions of crossing differential or difference Malmquist systems with certain types.In chapter 5,conclusion and prospect.