In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing sm...In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.展开更多
With the aid of Nevanlinna value distribution theory,differential equation theory and difference equation theory,we estimate the non-integrated counting function of meromorphic solutions on composite functional-differ...With the aid of Nevanlinna value distribution theory,differential equation theory and difference equation theory,we estimate the non-integrated counting function of meromorphic solutions on composite functional-differential equations under proper conditions.We also get the form of meromorphic solutions on a type of system of composite functional equations.Examples are constructed to show that our results are accurate.展开更多
基金partially supported by the NSFC(11271227,11271161)the PCSIRT(IRT1264)the Fundamental Research Funds of Shandong University(2017JC019)。
文摘In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.
基金This work was partially supported by NSFC of China(11271227,11271161)PCSIRT(IRT1264)+1 种基金the Fundamental Research Funds of Shandong University(2017JC019)NSFC of Shandong(ZR2018MA014).
文摘With the aid of Nevanlinna value distribution theory,differential equation theory and difference equation theory,we estimate the non-integrated counting function of meromorphic solutions on composite functional-differential equations under proper conditions.We also get the form of meromorphic solutions on a type of system of composite functional equations.Examples are constructed to show that our results are accurate.
