Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One

This paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem −u″(t)=λu(t)+g(t,u(t)), u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g...

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Main Authors:	José L. Gámez, Juan F. Ruiz-Hidalgo
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Journal of Function Spaces and Applications
Online Access:	http://dx.doi.org/10.1155/2012/284696

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spelling	doaj-951f5bd9c6c342189ce9ec857051a2e62020-11-24T23:24:36ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/284696284696Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension OneJosé L. Gámez0Juan F. Ruiz-Hidalgo1Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, SpainDepartamento de Didáctica de la Matemática, Facultad de Ciencias de la Educación, Campus de Cartuja, Universidad de Granada, 18071 Granada, SpainThis paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem −u″(t)=λu(t)+g(t,u(t)), u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g we obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems.http://dx.doi.org/10.1155/2012/284696
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	José L. Gámez Juan F. Ruiz-Hidalgo
spellingShingle	José L. Gámez Juan F. Ruiz-Hidalgo Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One Journal of Function Spaces and Applications
author_facet	José L. Gámez Juan F. Ruiz-Hidalgo
author_sort	José L. Gámez
title	Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One
title_short	Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One
title_full	Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One
title_fullStr	Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One
title_full_unstemmed	Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One
title_sort	bifurcation from infinity and resonance results at high eigenvalues in dimension one
publisher	Hindawi Limited
series	Journal of Function Spaces and Applications
issn	0972-6802 1758-4965
publishDate	2012-01-01
description	This paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem −u″(t)=λu(t)+g(t,u(t)), u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g we obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems.
url	http://dx.doi.org/10.1155/2012/284696
work_keys_str_mv	AT joselgamez bifurcationfrominfinityandresonanceresultsathigheigenvaluesindimensionone AT juanfruizhidalgo bifurcationfrominfinityandresonanceresultsathigheigenvaluesindimensionone
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Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One

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