Weakly nonlinear integral equations of the hammerstein type

Abstract

By using the theory of Moore-Penrose pseudoinverse operators, the nec- essary and sufficient conditions for the solvability of a weakly nonlinear integral equa- tion with a nondegenerate kernel are obtained. Equations for generating constants are constructed. A connection between the necessary and sufficient conditions has been established. The iterative procedure for finding a solution is proposed.