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Neutral Mixed Type Functional Differential Equations

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Abstract

We extend the existing Fredholm theory for mixed type functional differential equations developed by Mallet-Paret (J Dyn Differ Equ 11:1–47, 1999) to the case of implicitly defined mixed type functional differential equations. We present analogous results for the Fredholm alternative theorem, the cocycle property, and spectral flow property. In particular, we apply the theory to examples, one of which arises from modeling signal propagation in nerve fibers, and show the existence of traveling wave solutions via local continuation.

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Acknowledgments

This research was supported in part by NSF Grants DMS-0513438, DMS-0812800, and DMS-1115408.

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Authors and Affiliations

  1. Mathematics Department, Indiana University of Pennsylvania, Indiana, PA, 15705, USA

    Charles Lamb

  2. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Erik S. Van Vleck

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  1. Charles Lamb
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  2. Erik S. Van Vleck
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Correspondence to Erik S. Van Vleck.

Additional information

Dedicated to Professor John Mallet-Paret on the occasion of his 60th birthday.

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Lamb, C., Van Vleck, E.S. Neutral Mixed Type Functional Differential Equations. J Dyn Diff Equat 28, 763–804 (2016). https://doi.org/10.1007/s10884-015-9446-x

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  • DOI: https://doi.org/10.1007/s10884-015-9446-x

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