Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces-Reference-Cited by-同舟云学术

Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces

Published:2021-09-07 Issue:5 Volume:18 Page:
ISSN:1660-5446
Container-title:Mediterranean Journal of Mathematics
language:en
Short-container-title:Mediterr. J. Math.

Author:

Fonda Alessandro^ORCID,Klun Giuliano^ORCID,Sfecci Andrea^ORCID

Abstract

AbstractWe prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations.

Funder

Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00009-021-01857-8.pdf

Reference23 articles.

1. Amann, H., Ambrosetti, A., Mancini, G.: Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities. Math. Z. 158, 179–194 (1978)

2. Barbu, V.: Abstract periodic Hamiltonian systems. Adv. Differ. Equ. 1, 675–688 (1996)

3. Bebernes, J.W., Schmitt, K.: Periodic boundary value problems for systems of second order differential equations. J. Differ. Equ. 13, 32–47 (1973)

4. Boscaggin, A., Fonda, A., Garrione, M.: An infinite-dimensional version of the Poincaré–Birkhoff theorem. Ann. Scuola Norm. Pisa 20, 751–770 (2020)

5. De Coster, C., Habets, P.: Two-Point Boundary Value Problems. Lower and Upper Solutions. Elsevier, Amsterdam (2006)

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