ON SOLVABILITY OF URYSOHN-VOLTERRA
EQUATIONS WITH HYSTERESIS
IN WEIGHTED SPACES

MOHAMED ABDALLA DARWISH

Abstract:

This paper concerns the unique solvability of the nonlinear integral equations of the second kind with hysteresis of the form

$$y(t)=f(t)+\int^t_{-\infty}F(t,s,y(s),{\cal W}[S[y]](s))\,ds,\quad0\le t\le T$$

in weighted spaces. Also we have treated the case of nonlinear integral equations of the first kind with hysteresis.