A general multiplicity theorem for certain nonlinear equations in Hilbert spaces

Author:
Biagio Ricceri

Journal:
Proc. Amer. Math. Soc. **133** (2005), 3255-3261

MSC (2000):
Primary 47H50, 47J10, 47J30; Secondary 41A52, 41A65

DOI:
https://doi.org/10.1090/S0002-9939-05-08218-3

Published electronically:
June 20, 2005

MathSciNet review:
2161147

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove the following general result. Let be a real Hilbert space and a continuously Gâteaux differentiable, nonconstant functional, with compact derivative, such that

Then, for each for which the set is not convex and for each convex set dense in , there exist and such that the equation

has at least three solutions.

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Additional Information

**Biagio Ricceri**

Affiliation:
Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

Email:
ricceri@dmi.unict.it

DOI:
https://doi.org/10.1090/S0002-9939-05-08218-3

Keywords:
Nonlinear equations,
Hilbert spaces,
local and global minima,
critical points,
level sets,
minimax theory,
Chebyshev sets

Received by editor(s):
May 24, 2004

Published electronically:
June 20, 2005

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.