Existence results for the solution of abstract neutral impulsive differential problems with state-dependent delay. (English) Zbl 1530.34062
The aim of this paper is to prove the existence and uniqueness of mild solutions for some neutral impulsive differential equations with state-dependent delay. The linear part is assumed to generate an analytic semigroup on a Banach space. To prove the existence of a mild solution, the authors provide several conditions to allow them to apply Banach’s fixed point theorem or Schauder’s fixed point theorem. Application is given for illustration of the basic results of this work.
Reviewer: Khalil Ezzinbi (Marrakech)
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 34K40 | Neutral functional-differential equations |
| 34K45 | Functional-differential equations with impulses |
| 34K43 | Functional-differential equations with state-dependent arguments |
| 47H10 | Fixed-point theorems |
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