Linearized stability for nonlinear evolution equations

We present a general principle of linearized stability at an equilibrium point for the Cauchy problem u(t) + Au(t) There Exists 0, t greater than or equal to 0, u(0) = u(0), for an omega-accretive, possibly multivalued, operator A subset of X x X in a Banach space X, that has a linear 'resolvent-defivative' (A) over bar subset of X x X. The result is applied to derive linearized stability results for the case of A = (B + G) under 'minimal' differentiability assumptions on the operators B subset of X x X and G : cl D(B) --> X at the equilibrium point, as well as for partial differential delay equations.