Abstract
In this paper we study the existence of almost automorphic solutions for a class of linear neutral functional differential equations with finite delay and values in a Banach space. We show that the existence of an almost automorphic mild solution is related to the approximate controllability of a distributed control system. We applied our results to establish the existence of an almost automorphic solution for a neutral wave equation with delay.
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Henríquez, H.R., Cuevas, C. Almost automorphy for abstract neutral differential equations via control theory. Annali di Matematica 192, 393–405 (2013). https://doi.org/10.1007/s10231-011-0229-7
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DOI: https://doi.org/10.1007/s10231-011-0229-7
Keywords
- Neutral functional differential equations
- Equations in abstract spaces
- Almost automorphic functions
- Semigroups of operators
- Compact operators
- Controllability of systems