In this paper, we consider an abstract non-autonomous
evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r1),...,u((t-rn)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: Hna → H is a nonlinear mapping, r1,...,rn are nonnegative constants, and g(t)∈ C(□;H) is bounded. Motivated by [1] [2], we obtain the existence and stability of
synchronizing solution under some convergence condition. By this result, we
provide a general approach for guaranteeing the existence and stability of
periodic, quasiperiodic or almost periodic solution of the equation.
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