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

摘要

In this paper, the author will introduce the Sobolev space W12(Ωn) firstly and then give the reproducing properties of the space W12(Ωn). As these results of those, a class of the nonlinear operator equation ∑ni=1∏mij=1(Aiju)=f is transformed to the n-dimensional linear operator equation Au=f. Finally, we also give the exact solution of this nonlinear operator equation.