Regularity of solutions of nonlinear Volterra equations

Abstract.

We consider the regularity properties of solutions of the nonlinear Volterra equation¶¶$\frac{d}{dt}\left(u(t)-u_0+\int_0^t k(t-s)\left(u(s)-u_0\right)ds\right) + Au(t) \ni f(t)$¶¶in Banach spaces X without the Radon-Nikodym property. Existence of strong solutions for an m-completely accretive operator A in a normal Banach space $X\subset L^1(\Omega;\mu)$ is shown for sufficiently smooth data.