Perturbation of strongly continuous cosine family generators

Integrated cosine functions

“…In the case m 0, since loo 0 (see [9,Lemma]) and (b3) can be replaced by fg C(s)(X)ds 6-D(B) for > 0, Theorem 3.2 (with m 0) is consistent with [9, Pop.l.…”

“…In fact, set Px AR(A:, A) for A > w and y R(Ao, A)"'x for some Ao > w, then (Px + Pu)Y fF f2e-t-"c(m)(t)C(')(s)Ydsdt 2PaP.y (Pu-Px)Y + f fd e-'t-"'(C()(t + s)y + C()(I sl)y)dsdt for, > A > w, and so (8) It now follows from (9) that B Go(Y). The rest can be proved in [2,3].…”

О Свойствах Задачи Типа Коши Для Абстрактного Дифференциального Уравнения С Дробными Производными

“…Из (16), (17) вытекает справедливость требуемого неравенства (9), a вместе с ним и равномерная корректность задачи (6), (7).…”

“…превращается в соответствующий результат работы [17] о возмущении генератора КОФ ограниченным оператором.…”

Multiplicative perturbations of local C-cosine functions

“…Moreover, a local C-cosine function is not necessarily extendable to the half line [0, ∞) (see [22]) except for C = I (identity operator on X). Perturbations of local C-cosine functions with or without the exponential boundedness have been extensively studied by many authors appearing in [2,6,[8][9][10][11][12][13][14][15][16][17]19,23,25]. Some interesting applications of this topic are also illustrated there.…”