Periodic solutions to second-order nonlinear differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Periodic solutions to second-order nonlinear differential equations in Banach spaces
zbMATH Open document ID: 1494.34134
author: David Ariza-Ruiz
author: Jesus García-Falset
published in: Mediterranean Journal of Mathematics
publication date: 2022-03-14T00:00:00Z
review text: In this paper, the authors study the following second-order dynamic differential equation: \[\begin{cases} u''(t) = f(t, u(t)) + h(t),\\ u(a)-u(b)=u'(a)-u'(b)=0, \end{cases} \] where \(f : [a,b]\times {\mathbb B} \to {\mathbb B}\) is a sequentially weak-strong continuous mapping, \(h : [a,b] \to {\mathbb B}\) is a continuous function on \({\mathbb B}\) and \({\mathbb B}\) is a reflexive real Banach space. The existence of periodic solutions is proved via a generalization of Bolzano-Poincaré-Miranda theorem and Leray-Schauder alternative theorem, under the boundedness and growth conditions. Moreover, three examples are presented, two for systems of second-order differential equations and one for a partial differential equation, illustrating the obtained result.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7488607
zbMATH Keywords: second-order differential equations
zbMATH Keywords: periodic solutions
MaRDI profile type: Publication
full work available at URL: s00009-021-01956-6
OpenAlex ID: W4211159792
Wikidata QID: Q115390233
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DOI: 10.1007/S00009-021-01956-6
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description: scientific article; zbMATH DE number 7488607