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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Max-Min characterization of the mountain pass energy level for a class of variational problems


Authors: Jacopo Bellazzini and Nicola Visciglia
Journal: Proc. Amer. Math. Soc. 138 (2010), 3335-3343
MSC (2000): Primary 58E05; Secondary 35J20, 35J60
Published electronically: April 29, 2010
MathSciNet review: 2653963
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Abstract: We prove the existence of a critical point at the mountain pass energy level for a general class of variational problems. We also provide a Max-Min characterization of the mountain pass energy level. Finally, we present some concrete applications.


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Additional Information

Jacopo Bellazzini
Affiliation: Dipartimento di Matematica Applicata, Università di Pisa, Via Buonarroti 1/C, 56127 Pisa, Italy
Email: j.bellazzini@ing.unipi.it

Nicola Visciglia
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56100 Pisa, Italy
Email: viscigli@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10415-8
PII: S 0002-9939(10)10415-8
Keywords: Critical point theory, mountain pass energy level, nonlinear elliptic equations
Received by editor(s): June 24, 2009
Received by editor(s) in revised form: September 4, 2009, and December 16, 2009
Published electronically: April 29, 2010
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.