Neutral Mixed Type Functional Differential Equations

摘要

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.