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

摘要

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].