ABSTRACT NON-LINEAR VOLTERRA EQUATION

The existence, uniqueness, regularity and dependence upon data of solutions of the abstract Volterra equation u(t)+∫ 0 t a(t-s)A(u(s))ds∈f(t), t≧0 are studied in a real Banach space. The nonlinear operator A is assumed to be m-accretive and the assumptions on the kernel a do not exclude the possibility that lim t→0+ a(t)=+∞. © 1979 Hebrew University.