Fredholm Alternative is a classical tool of periodic linear equations, allowing to describe the existence of periodic solutions of an inhomogeneous equation in terms of the adjoint equation. A few partial extensions have been proposed in the literature for recurrent equations: our aim is to point out that they have a common root and discuss whether such a root gives rise to a general Fredholm-type Alternative. Sacker–Sell spectral theory and Favard theory are main ingredients in this discussion: a considerable effort is devoted to understand how Favard theory is affected by adjunction, at least for planar equations.
Favard theory for the adjoint equation and Fredholm Alternative / C. J., O. R., M.E. Tarallo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 262:2(2017 Jan 15), pp. 749-802. [10.1016/j.jde.2016.09.041]
Favard theory for the adjoint equation and Fredholm Alternative
M.E. Tarallo
2017
Abstract
Fredholm Alternative is a classical tool of periodic linear equations, allowing to describe the existence of periodic solutions of an inhomogeneous equation in terms of the adjoint equation. A few partial extensions have been proposed in the literature for recurrent equations: our aim is to point out that they have a common root and discuss whether such a root gives rise to a general Fredholm-type Alternative. Sacker–Sell spectral theory and Favard theory are main ingredients in this discussion: a considerable effort is devoted to understand how Favard theory is affected by adjunction, at least for planar equations.File | Dimensione | Formato | |
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