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-2(1)(Omega(n)) firstly and then give the reproducing properties of the space W-2(1) (Omega(n)). As these results of those, a class of the nonlinear operator equation Sigma(i=1)(n) Pi(j=1)(mi) (A(ij)u) = f is transformed to the n-dimensional linear operator equation Au = f. Finally, we also give the exact solution of this nonlinear operator equation. (C) 2002 Published by Elsevier Science Inc.