Almost periodic solutions for nonlinear delay evolutions with nonlocal initial conditions
نویسنده
چکیده
We consider the nonlinear delay differential evolution equation { u′(t) ∈ Au(t)+ f (t, ut ), t ∈ R+, u(t) = g(u)(t), t ∈ [−τ, 0], where τ ≥ 0, X is a real Banach space, A is the infinitesimal generator of a nonlinear semigroup of contractions whose Lipschitz seminorm decays exponentially as t → e−ωt when t → +∞ and f : R+×C([−τ, 0]; D(A)) → X is jointly continuous. We prove that if f Lipschitz with respect to its second argument and its Lipschitz constant satisfies the condition eωτ < ω, g : Cb([−τ,+∞); D(A)) → C([−τ, 0]; D(A)) is nonexpansive and (I − A)−1 is compact, then the unique C0-solution of the problem above is almost periodic.
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تاریخ انتشار 2013