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

On strongly indefinite functionals with applications


Author: Helmut Hofer
Journal: Trans. Amer. Math. Soc. 275 (1983), 185-214
MSC: Primary 58E05; Secondary 35L70, 47H15
MathSciNet review: 678344
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Abstract: Recently, in their remarkable paper Critical point theory for indefinite functionals, V. Benci and P. Rabinowitz gave a direct approach--avoiding finite-dimensional approximations--to the existence theory for critical points of indefinite functionals. In this paper we develop under weaker hypotheses a simpler but more general theory for such problems. In the second part of the paper the abstract results are applied to a class of resonance problems of the Landesman and Lazer type, and moreover they are illustrated by an application to a wave equation problem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0678344-2
PII: S 0002-9947(1983)0678344-2
Keywords: Critical point theory, resonance problem, wave equation
Article copyright: © Copyright 1983 American Mathematical Society