Nonlinear Functional Evolutions in Banach Spaces

Finite extinction and null controllability via delayed feedback non-local actions

“…This means that as long as the delay term appears, as above, in the equation we do not need the full machinery of the theory of abstract functional differential equations as developed, for instance, in Ha [5], and we can guarantee the existence and uniqueness of mild solutions for every continuous initial function φ. By ''mild (or integral) solution'' we understand a continuous function u : [0, T ) → X which satisfies…”

Existence and Asymptotics of Abstract Functional Differential Equations

“…As (u n ) |I = ϕ it remains to consider t ∈ J. From ( 12) we obtain with the definition of the operator T λ,ϕ given by (8),…”

“…By [16, Theorem 2.9] v n = lim λ→0 v n,λ is the integral solution in the sense of Definition 7.10 with For related results compare the studies of Ghavidel [5], Ghavidel/Ruess [6], Kartsatos [11], Kartsatos/Liu [13], Kartsatos/Parrot [12], Jeong/Shin [10], Ruess/Summers [21], [22], and Tanaka [24]. Moreover, the equation is discussed in the textbook [8].…”