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