, Volume 11, Issue 1, pp 1-47

The Fredholm Alternative for Functional Differential Equations of Mixed Type

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Abstract

We prove a Fredholm alternative theorem for a class of asymptotically hyperbolic linear differential difference equations of mixed type. We also establish the cocycle property and the spectral flow property for such equations, providing an effective means of calculating the Fredholm index. Such systems can arise from equations which describe traveling waves in a spatial lattice.