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  • 1
    Electronic Resource
    Electronic Resource
    The Fredholm Alternative for Functional Differential Equations of Mixed Type (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 1-47 
    Details
    ISSN: 1572-9222
    Keywords: Fredholm alternative ; exponential dichotomy ; functional differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021889401235
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 49-127 
    Details
    ISSN: 1572-9222
    Keywords: Traveling waves ; spatially discrete systems ; lattice differential equations ; continuation methods ; heteroclinic orbits ; Lin's method ; Mel'nikov method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely, lattice differential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c≠0, are also shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where c≠0. Convergence results for solutions are obtained at the singular perturbation limit c → 0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021841618074
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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