Abstract
We study a Cauchy problem associated to a second-order integro-differential inclusion. The general framework of evolution operators that define the problem that we consider has been developed by Kozak and, afterwards, improved by Henriquez. Our aim is to show the existence of mild solutions continuously depending on a parameter for the problem studied in the case when the set-valued map is Lipschitz in state variables. Moreover, as a consequence, we deduce the existence of a continuous selection of the set of all mild solutions of the problem considered. The proof our main result is based on a result of Bressan and Colombo concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values.
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Cernea, A. (2018). Continuous Selections of Solution Sets of a Second-Order Integro-Differential Inclusion. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_5
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DOI: https://doi.org/10.1007/978-3-319-75647-9_5
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