Favard theory for the adjoint equation and Fredholm Alternative

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• 作者：Juan Campos^a ; ^{campos@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; Rafael Obaya^b ; ¹ ; ^{rafoba@wmatem.eis.uva.es" class="auth_mail" title="E-mail the corresponding author} ; Massimo Tarallo^c ; ^{massimo.tarallo@unimi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34C27 ; 34B05 ; 34A30 ; 34D09
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：262
• 期：2
• 页码：749-802
• 全文大小：652 K

文摘

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.