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Positive subharmonic solutions to nonlinear ODEs with indefinite weight

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dc.contributor.author Boscaggin, Alberto
dc.contributor.author Feltrin, Guglielmo
dc.date.accessioned 2016-11-21T08:00:00Z
dc.date.available 2016-11-21T08:00:00Z
dc.date.issued 2017
dc.identifier.citation Commun. Contemp. Math. en_US
dc.identifier.issn 02191997
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/35265
dc.identifier.uri https://arxiv.org/abs/1605.02500
dc.description AMS Subject Classification: Primary: 34C25; Secondary: 34B18, 37J10, 47H11. en_US
dc.description.abstract We prove that the superlinear indefinite equation u"+a(t)up=0, where p>1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫a(t) dt<0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by G. J. Butler in its pioneering paper (JDE, 1976). The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré-Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it). en_US
dc.description.sponsorship Work performed under the auspicies of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Guglielmo Feltrin and Alberto Boscaggin are partially supported by the GNAMPA Project 2016 “Problemi differenziali non lineari: esistenza, molteplicità e proprietà qualitative delle soluzioni”. Alberto Boscaggin also acknowledges the support of the project ERC Advanced Grant 2013 n. 339958 “Complex Patterns for Strongly Interacting Dynamical Systems - COMPAT”. en_US
dc.language.iso en en_US
dc.publisher World Scientific Publishing en_US
dc.relation.ispartofseries Communications in Contemporary Mathematics;
dc.subject subharmonics en_US
dc.subject indefinite weight en_US
dc.subject Poincaré-Birkhoff theorem en_US
dc.subject Morse index en_US
dc.subject coincidence degree en_US
dc.title Positive subharmonic solutions to nonlinear ODEs with indefinite weight en_US
dc.type Article en_US
dc.subject.miur MAT/05 en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.identifier.arXiv 1605.02500

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