The exact solution of nonlinear operator equation AuBu+Cu=f

This paper is intended to discuss the problems of solving system of linear operator equations and a kind of nonlinear operator equation AuBu+Cu=f. For system of linear operator equations, we obtain a criterion about the existence of solutions. If it has solutions, we get the analytic representation of its minimum norm solution and the structure of its solution space; for nonlinear operator equation AuBu+Cu=f, with the help of the discussion on how to solve the system of linear operator equations, the exact solution is given. Besides, we obtain the representation of all its solutions.