Abstract
In this paper we shall first prove an existence result for an implicit functional equation. The proof is based on a fixed point result in a Banach lattice derived in [1]. The so obtained implicit function theorem is then applied to an initial value problem of an implicit functional differential equation. The functions in the considered equations may be discontinuous in all their arguments. Special cases and a concrete example are given to demonstrate the obtained results.
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References
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Heikkilä, S. (2004). Implicit Function Theorems and Discontinuous Implicit Differential Equations. In: Constanda, C., Largillier, A., Ahues, M. (eds) Integral Methods in Science and Engineering. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8184-5_14
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DOI: https://doi.org/10.1007/978-0-8176-8184-5_14
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6479-8
Online ISBN: 978-0-8176-8184-5
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