On strongly indefinite functionals with applications

Author:
Helmut Hofer

Journal:
Trans. Amer. Math. Soc. **275** (1983), 185-214

MSC:
Primary 58E05; Secondary 35L70, 47H15

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678344-2

MathSciNet review:
678344

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-1983-0678344-2

Keywords:
Critical point theory,
resonance problem,
wave equation

Article copyright:
© Copyright 1983
American Mathematical Society