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

Authors:
Chun-li Li;Ming-gen Cui
Affiliations:
Automation College, Harbin Engineering University, Harbin 150001, Heilongjiang, China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

In this paper, the author will introduce the Sobolev space W21 (Ωn) firstly and then give the reproducing properties of the space W21 (Ωn). As these results of those, a class of the nonlinear operator equation Σi=1n Πj=1mi (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.