In this paper we study existence and uniqueness of solutions for the Hammerstein equation u(x)=v{x) + X K{x,y)f{y,u{y))dy, a; €/* := [ai,6i] x [02, 62] , in the space BV^{I^) of function of bounded total (^-variation in the sense of Riesz, where A 6 E, /f : /¿ x /* -» E and / : /¿ x E -> M are suitable functions. 2010 Mathematics Subject Classification: primary 45G10. Key words and phrases: existence and uniqueness of solutions of the Hammerstein integral equation in the plane, i^-bounded total variation norm on a rectangle.
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