United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SOLVABILITY OF URYSOHN AND URYSOHN-VOLTERRA EQUATIONS WITH HYSTERESIS IN WEIGHTED SPACES

Abstract The existence of solutions to nonlinear integral equations of the second kind with hysteresis, of Urysohn-Volterra and Urysohn types has been established. We develop the solvability theory of Urysohn-Volterra equation with hysteresis in weighted spaces proposed by the author [M.A. Darwish, On solvability of Urysohn-Volterra equations with hysteresis in weighted spaces, J