The Value Distribution Of Meromorphic Solutions Of Systems Of Higher Order Non-linear Differential Equations

The problem of systems of complex differential equations is a fringe field which rose from the end of 80's last century,its study requires multi-subject.The main tool of the study is the theorem of Nevanlinna value distribution,Wiman-Valiron theorem etc.Many scholars introduce the notion of admissible solution on their study of the systems of some algebra differential equations,some references has deeply investigate these problems.In this paper, using the theory and the method of the value distribution of mero-morphic functions, we investigate the problem of the value distribution of meromorphic solutions of systems of higher order non-linear algebraic differential equations and obtain some results,namely,if the systems of this equations meets some condition,then the counting function of admissible parameters at least M multiplicity of its poles N₍(M)(r,w) is small functions,which M is some constant;and discuss the problem of admissible solution of systems of higher order non-linear algebraic differential equations and obtain a result similar to Malmquist theorem,namely,if the systems of this equations meets some condition,and admits admissible solutions,then there is some connection between the offset quantity of the admissible parameters and the power of the equation.