Global existence, uniqueness, and continuous dependence for a semilinear initial value problem

Abstract

In this paper, we consider the semilinear initial value problem associated with an operator A whose spectrum lies in a sector of the complex plane and whose resolvent satisfies ‖(z−A)−1‖⩽M|z|γ for some −1<γ<0 and all z outside the sector. The properties of existence and uniqueness of global mild solutions and continuous dependence on the initial data are investigated.