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Zbl 0927.34049
Mallet-Paret, John
The Fredholm alternative for functional-differential equations of mixed type. (English)
[J] J. Dyn. Differ. Equations 11, No.1, 1-47 (1999). ISSN 1040-7294; ISSN 1572-9222/e

A Fredholm alternative theorem for a class of asymptotically hyperbolic linear differential-difference equations of mixed type is proved. The cocycle property and the spectral flow property for such equations, providing an effective mean of computing the Fredholm index, are established. The asymptotic behavior of solutions is discussed, too. The considered systems can arise from equations which describe traveling waves in a spatial lattice.
[J.Diblík (Brno)]

MSC 2000:: *34K05 General theory of functional-differential equations
35L05 Wave equation
34D09 Dichotomy, trichotomy

Keywords: Fredholm alternative; exponential dichotomy; functional-differential equations; asymptotic behavior of solutions

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