Existence Results for Initial Value Problems for Neutral Functional Differential Equations

Existence of Solutions of Nonlinear Neutral Integrodifferential Equations in Banach Spaces

“…The theory of neutral delay differential equations has been extensively studied in the literature [1,2,[7][8][9]. Hernandez and Henriquez [5] obtained some existence results for neutral functional differential equations in Banach spaces, and in [6] they established the existence of periodic solutions for the same kind of equations.…”

Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays

“…We get that the IVP (1.1)-(1.2) corresponding to parameter γ has a unique solution x(t; γ ) for t ∈ [−r,α] for somẽ α =α(γ ) > 0. Moreover, the above method of steps argument yields easily that 2,5) are open sets in C and R n , respectively. Clearly, M 2 and M 5 are compact subsets of R n .…”

“…(1.1) can be considered as a natural "generalization" of the "usual" NFDEs with time-dependent delays of the form d dt D(t, x t ) = f (t, x t ), (1.4) but (1.4) may also contain (1.1) depending on appropriate conditions on D and f , like in [22]. The basic well-posedness theory for several classes of (1.4), especially for the linear case, is well-developed [2,5,14,16,31]. Existence, uniqueness and numerical approximation of solutions was studied in [20] for SD-NFDEs of the form d dt…”

Existence result for nonlinear neutral integrodifferential equations with distributed delays

“…Several authors have studied the existence of solutions of nonlinear neutral differential equations in Banach space, (Hernandez and Henriquez, 1998;Balachandran and Sakthivel, 1999;Balachandran et. al., 2006;Balachandran and Park, 2003;Arino et. al., 1997).…”