Data di Pubblicazione:
2017
Citazione:
Asymptotically dichotomic almost periodic differential equations / J. Campos, M. Tarallo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 263:2(2017), pp. 1323-1386.
Abstract:
Consider a non-linear differential equation in RNwhich asymptotically behaves as a linear equation admitting an exponential dichotomy. We wonder if almost periodic solutions exist when we add to the equation an almost periodic forcing term, large enough and not vanishing too much. A positive answer has been given in [3] for the scalar case N=1 and our aim is to extend that result to higher dimensions. We discover that the extension seems to be driven by a new ingredient, namely the type of the exponential dichotomy: besides the pure stable types, the mixed hyperbolic type is now possible and leads to a weaker than expected extension. An example shows that a stronger extension cannot be obtained by the same method. The approach is blended and mixes methods of differential equations and functional analysis, especially when estimating norm and spectral radius of some crucial positive but non-compact linear integral operators.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Almost periodic solutions; Contractions and Fixed points; Exponential dichotomies; Haar measure; Positive operators; Spectral radius; Analysis
Elenco autori:
J. Campos, M. Tarallo
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