The necessary and sufficient condition for the existence and the uniqueness ofsolution of the continuous linear operator equation is given. We give also minimalnorm solution(or generalized) of the equation. Further, we construct a reproducingkernel space W21(Ω)and give the reproducing kerne of the space W21(Ω). In thespace W21(Ω), we study the problem of solving a class nonlinear operator equation.Some examples are also given illustrate of this theory.
