Fermat型q-差分微分方程的整函数解OA

Utilizing Nevanlinna and complex differential-difference equations theory,the precise ana-lytic forms of transcendental entire solutions are explored for Fermat type equations of the form[f(K)(z)]2+[f(qz+c)-f(z)]2=Q(z)involving q-difference and derivatives.Firstly,system of equations sat-isfying the solution are obtained by Hadamard factorization theorem,and the concrete forms of f(K)(z)and f(qz+c)-f(z)are calculated.Secondly,in the equation that the sum of the function fj(z)(j=1,2,3)is 1,the uniqueness theorem of meromorphic function is used to judge that the two functions in fj(z)(j=1,2,3)are identical to 1,and the discussion is divided into two cases.Finally,in each case,k is odd and even,and the relationship between the variables is obtained.Thereby leads to more ideas and techniques for studying solutions of complex differential-difference equations in future research.