Abstract
Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.
Highlights
In this work we shall prove the existence of solutions of a functional differential inclusion
Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay
We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions
Summary
In this work we shall prove the existence of solutions of a functional differential inclusion. Complicated situations in which the delay depends on the unknown functions have been proposed in modeling in recent years. These equations are frequently called equations with state-dependent delay. Existence results and among other things were derived recently for functional differential equations when the solution is depending on the delay on a bounded interval [0, b] for impulsive problems. To the best of our knowledge, there exist very few papers devoted to functional evolution inclusions with state-dependent delay on unbounded intervals. Those results are stated in the Frechet space setting. The present results initiate the study of such problems in the Banach space setting
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