Entire Function Solutions Of Several Types Of Functional Equations

In this paper, we study the entire function solutions of several types of functional equation, by the method of R.Nevanlinna the value distribution theory of meromorphi-c functions. For the nonlinear complex differential equation-sin2n z and (where n is an positive integer), we proved that the entire function solution both are trivial. We generalize the relevant conclusions of L.ping and C.C.Yang about entire function solution of differential equation For nonconstant polynomial p(z), L.ping and C.C.Yang conjectured differential equation f(z)fn(z)=sin2z+p(z) has no entire function solutions. For the speculation, we can obtain the entire function solution of f(z)fn(z)=sin2z-1by discussing the case of p(z) is non-zero constant.In addition, We also study the entire function solutions of Fermat type Diophantine functional equations we have proved that were not the entire function solutions of the functional equation if growth order of nonconstant entire function f(z), g(z), h(z) is less than4/3,and f(z) has at least one zero with multiplicity.