id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-2456	Baghli, Selma Bendimerad; Aoued, Djillali	Controllability of Mild Solutions for Evolution Equations with Infinite State-Dependent Delay	2016	19	.pdf	application/pdf	7547	482	81	We consider the function eu(t) := supθ∈[0,t] |z(θ )| then by the nondecreasing character of ψ, we obtain for βn := � (ÒM + 1)M0 L + ÒM Ln � � ÒM eM eM1n+ 1 � + ÒM eM eM1n � 1+ KnM0 L � |by| + �� ÒM eM eM1n+ 1 � M0 L � ÒM +Mn +L φ � + ÒMH � ÒM eM eM1nM0 LKn �� ‖φ‖B and for λ < 1, eu(t) λ � 1−M0 LKn � ≤βn + ÒM L � ÒM eM eM1n+ 1 � ∫ n 0 � Kneu(s) Then the evolution problem (13) is con- trollable on R. Example 2 Consider the semilinear neutral evolution equation ∂ ∂ t � u(t,ξ)− ∫ 0 −∞ a3(s− t)u � s−ρ1(t)ρ2 �∫ π 0 a2(θ )|u(t,θ )|2dθ � ,ξ � ds � = ∂ 2u(t,ξ) ∂ ξ2 + a0(t,ξ)u(t,ξ) + ∫ 0 −∞ a1(s− t)u � s−ρ1(t)ρ2 �∫ π 0 a2(θ )|u(t,θ )|2dθ � ,ξ � ds, for t ≥ 0, ξ ∈	cache/ejpam-2456.pdf	txt/ejpam-2456.txt