Accretive sets and differential equations in Banach spaces

This paper is concerned with global solutions of the initial value problem (1)du/dt +Au∋0, u(0)=x where A is a (nonlinear) accretive set in a Banach space X. We show that various approximation processes converge to the solution (whenever it exists). In particular we obtain an exponential formula for the solutions of (1). Assuming X* is uniformly convex, we also prove the existence of a solution under weaker assumptions of A than those made by previous authors (F. Browder, T. Kato).