Parameter identification in classes of neutral differential equations with state-dependent delays

Controllability of Second-Order Impulsive Functional Differential Equations With State-Dependent Delay

“…Arguing as in the proof of Theorem 3.8, we can prove that Ψ(·) is a condensing map on B r (y |I , Y ) and, from Lemma 2.5, we conclude that there exists a mild solution x(·) for (9)- (12 …”

“…Functional differential equations with statedependent delay have become more important in some mathematical models of real phenomena. The reader is referred to [1,4,5,7,8,[11][12][13][14]32] and references therein for some examples and applications. The problem of the existence of solutions of functional differential equations with state-dependent delay has been treated recently in [2,[16][17][18][19][20]25].…”

“…The literature related to second order nonlinear systems with state-dependent delay is not vast, to our knowledge, in the recent works [6,15]. We also cite [9,12,35] for the case of neutral differential equations with dependent delay. To the best of our knowledge, the study of controllability of abstract nonlinear second order impulsive systems with state-dependent delay is an almost untreated topic in the literature and this fact is the main motivation for this article.…”

“…This fixed point x(·) is then a mild solution of the system (9)- (12). Clearly, (Ψx)(a) = x 1 , which means that the control u steers the system from the initial state φ to x 1 in time a, provided we can obtain a fixed point of the operator Ψ which implies that the system is controllable.…”

Teoria de semigrupos e aplicações a equações impulsivas com retardamento dependendo do estado

“…onde Aé o gerador infinitesimal de um C 0 -semigrupo compacto de operadores lineares limitados (T (t)) t≥0 definidos em um espaço de Banach X; as funções Equações funcionais com retardo dependendo do estado têm sido estudadas em diversos trabalhos, veja entre outros [1,2,3,5,6,11,12,28,30]. O estudo de sistemas em derivadas parciais com retardo dependendo do estado iniciou-se recentemente e, ao nosso entender, a literatura existente está limitada aos artigos Hernández, Prokopczyk & Ladeira [16] e Wu & Rezounenko [31].…”