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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Strongly indefinite systems with critical Sobolev exponents
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by Josephus Hulshof, Enzo Mitidieri and Robertus vanderVorst PDF
Trans. Amer. Math. Soc. 350 (1998), 2349-2365 Request permission

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.
References
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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
  • Received by editor(s): June 5, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2349-2365
  • MSC (1991): Primary 35J50, 35J55, 35J65
  • DOI: https://doi.org/10.1090/S0002-9947-98-02159-X
  • MathSciNet review: 1466949