A class of nonlinear evolution equations subjected to nonlocal initial conditions

We prove the existence of C0C0-solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions, of the form: {u′(t)+Au(t)∋f(t)f(t)∈F(t,u(t))u(0)=g(u), where A:D(A)⊆X↝XA:D(A)⊆X↝X is an mm-accretive operator acting on the infinite-dimensional Banach space XX, F:[0,2π]×D(A)¯↝X is an almost strongly weakly u.s.c. multi-function which satisfies an appropriate “sign” condition, while g:C([0,2π];D(A)¯)→D(A)¯ is a continuous function.