Solvability of Urysohn and Urysohn-Volterra equations with hysteresis in weighted spaces

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. Integral Equat. Appl. 14 (2) (2002), 151-163].