Multiplicity of solutions for gradient systems

We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resona...

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Bibliographic Details
Main Author:	Edcarlos D. Da Silva
Format:	Article
Language:	English
Published:	Texas State University 2010-05-01
Series:	Electronic Journal of Differential Equations
Subjects:	Critical groups resonance indefinite weights Morse theory
Online Access:	http://ejde.math.txstate.edu/Volumes/2010/64/abstr.html

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spelling	doaj-449fa47047d84a2fa994743b23cacab32020-11-24T23:42:32ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-05-01201064,115Multiplicity of solutions for gradient systemsEdcarlos D. Da SilvaWe establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation of critical groups. http://ejde.math.txstate.edu/Volumes/2010/64/abstr.htmlCritical groupsresonanceindefinite weightsMorse theory
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Edcarlos D. Da Silva
spellingShingle	Edcarlos D. Da Silva Multiplicity of solutions for gradient systems Electronic Journal of Differential Equations Critical groups resonance indefinite weights Morse theory
author_facet	Edcarlos D. Da Silva
author_sort	Edcarlos D. Da Silva
title	Multiplicity of solutions for gradient systems
title_short	Multiplicity of solutions for gradient systems
title_full	Multiplicity of solutions for gradient systems
title_fullStr	Multiplicity of solutions for gradient systems
title_full_unstemmed	Multiplicity of solutions for gradient systems
title_sort	multiplicity of solutions for gradient systems
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2010-05-01
description	We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation of critical groups.
topic	Critical groups resonance indefinite weights Morse theory
url	http://ejde.math.txstate.edu/Volumes/2010/64/abstr.html
work_keys_str_mv	AT edcarlosddasilva multiplicityofsolutionsforgradientsystems
_version_	1725504049121329152

Multiplicity of solutions for gradient systems

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