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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Strongly indefinite systems
with critical Sobolev exponents


Authors: Josephus Hulshof, Enzo Mitidieri and Robertus vanderVorst
Journal: Trans. Amer. Math. Soc. 350 (1998), 2349-2365
MSC (1991): Primary 35J50, 35J55, 35J65
MathSciNet review: 1466949
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Abstract: We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.


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Additional Information

Josephus Hulshof
Affiliation: Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Email: hulshof@wi.leidenuniv.nl

Enzo Mitidieri
Affiliation: Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piazzale Europa 1, 34100 Trieste, Italy

Robertus vanderVorst
Affiliation: Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30332-0190
Email: rvander@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02159-X
PII: S 0002-9947(98)02159-X
Keywords: Elliptic variational systems, strongly indefinite functionals, dual method, critical Palais-Smale level, critical points, ground states, decay rates, scaling
Received by editor(s): June 5, 1996
Article copyright: © Copyright 1998 American Mathematical Society