Abstract
In this paper, we investigate the existence of solutions for a class of second-order impulsive neutral functional differential inclusions in Banach spaces. Sufficient conditions for the existence are derived with the help of the fixed point theorem for multivalued maps due to Dhage.
Highlights
1 Introduction In this paper, we shall study a class of initial value problems for second-order impulsive neutral functional differential inclusions in Banach spaces described in the form g(t, yt)] ∈ Ik (y(tk– )), F(t, yt), k =
By means of a fixed point theorem for condensing multivalued map, solvability of impulsive neutral evolution differential inclusions with statedependent delay has been given by the authors in [ ]
Recently much attention has been paid to using a fixed point theorem for multivalued maps due to Dhage to solve the problem for impulsive differential inclusions
Summary
1 Introduction In this paper, we shall study a class of initial value problems for second-order impulsive neutral functional differential inclusions in Banach spaces described in the form g(t, yt)] ∈ Ik (y(tk– )), F(t, yt), k = , . Where F : J × D → P(E) is a multivalued map, g : J × D → E is a given function, D = {ψ : [–r, ] → E | ψ is continuous everywhere except for a finite number of points s at which ψ(s) and the right limit ψ(s+) exist and ψ(s–) = ψ(s)}, φ ∈ D ( < r < ∞), P(E) is the family of all subsets of E, = t < t < · · · < tm < tm+ = T , Ik : E → E
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