The exact solution for solving a class nonlinear operator equations in the reproducing kernel space

In this paper, the author will introduce the Sobolev space W^1"2(@W^n) firstly and then give the reproducing properties of the space W^1"2(@W^n). As these results of those, a class of the nonlinear operator equation @?^n"i"="1@?^m^"^i"j"="1(A"i"ju)=f is transformed to the n-dimensional linear operator equation Au=f. Finally, we also give the exact solution of this nonlinear operator equation.