Asymptotic properties of functional differential equations in Banach spaces (Q1423950)

The author studies the asymptotic properties of the following abstract nonlinear functional differential equation \[ \frac{d}{dt}u^i(t) = A_iu^i(t) + f_i(t,u_t^1,...,u_t^m), \quad t \geq t_0, \] \[ u^i(t_0 + s) = \phi_i(s), \quad -a \leq s \leq 0, \] where \(A_i\) is a suitable closed linear operator generating a \(C_0\)-semigroup. Criteria for invariant and attracting sets are obtained in the paper. Adequate examples illustrate the obtained results.