Nonlinear Hammerstein equations and functions of bounded Riesz-Medvedev variation

Jürgen Appell, Tomas Dominguez Benavides



In this paper we study the solvability of a nonlinear Hammerstein type integral equation in the space of functions of bounded Riesz-Medvedev variation. To this end, we derive a compactness criterion and apply Schauder's fixed point theorem to a suitable operator whose fixed points coincide with the solutions of the integral equation.


Bounded variation; nonlinear integral equation; fixed point theorem; Orlicz space

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