On explicit abstract neutral differential equations with state-dependent delay II. (English) Zbl 07892871
The authors study existence and uniqueness of a solution for abstract neutral equations in Banach spaces and with a state-dependent delay:
\begin{gather*}
u'(t)=Au(t)+F(t,u(\sigma(t,u(t)),u'(\sigma(t,u(t))),\\
u_0=\varphi\in C([-p,0], X).
\end{gather*}
The main results were illustrated by an interesting example.
Reviewer: Leonid Berezansky (Be’er Sheva)
MSC:
| 34K43 | Functional-differential equations with state-dependent arguments |
| 34K30 | Functional-differential equations in abstract spaces |
| 34K40 | Neutral functional-differential equations |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
neutral equations with state-dependent delay; existence and uniqueness; equations in Banach spaceReferences:
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