id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1344	Zhou, Yao; Liu, Hongliang	Upper semicontinuity of uniform attractors for singular perturbed second order nonautonomous delay lattice systems	2025	22	.pdf	application/pdf	10893	452	82	+ ∫ t t−ϑ ∥u̇ϵ(r)∥2dr ≤ ϑK̃3(ϵ, q1), t ∈ R. EJDE-2025/64 ATTRACTORS FOR DELAY LATTICE SYSTEMS 15 Then for t ∈ R, ϵ ∈ (0, ϵ], we have∫ t+1 t ∥u̇ϵ(r)∥2dr ≤ K̃3(ϵ, q1) + ϵ∥u̇ϵ(t)∥2 ≤ K̃3(ϵ, q1) + C1(q1) +M1 . In view of [3, 4, 27], for any g ∈ H(g0), t ∈ R, {Ag 0,t}t∈R is the pullback attractor of {Ug0 (t, τ)}t≥τ and Ag 0,t = {ut|{ut(·), t ∈ R} is a complete bounded trajectory of {Ug0 (t, τ)}t≥τ} = ∩r≥0∪s≥rUg0 (t, t− s)B0 ⊂ B0 ⊂ ℓ2ϑ. that is, for all g ∈ H(g0), t ∈ R, Ag 0,t is compact in ℓ2ϑ; for all t ≥ τ ∈ R, Ug0 (t, τ)A g 0,τ = Ag0,t; for all B ⊂ B(ℓ2ϑ), lims→+∞ dh(U g 0 (t, t − s)B,Ag0,t)	cache/ejde-1344.pdf	txt/ejde-1344.txt