Some abstract critical point theorems and applications

Anna Maria Candela; Giuliana Palmieri

doi:10.3934/proc.2009.2009.133

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2009, Volume 2009: 133-142. Doi: 10.3934/proc.2009.2009.133 open access

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Some abstract critical point theorems and applications

Anna Maria Candela^1, and
Giuliana Palmieri^2,

1.
Dipartimento Di Matematica, Universita' degli Studi di Bari "Aldo Moro", via E. Orabona 4, 70125 Bari
2.
Dipartimento Di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari

Received: June 30, 2008

Revised: February 28, 2009

Published: August 2009

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Abstract

Since Palais' pioneer paper in 1963, Condition $(C)$ in both the Palais--Smale version and Cerami's variant has been widely used in order to prove minimax existence theorems for $C^1$ functionals in Banach spaces. Here, we introduce a weaker version of these conditions so that a Deformation Lemma still holds and some critical points theorems can be stated. Such abstract results apply to $p$--Laplacian type elliptic problems.

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Mathematics Subject Classification: Primary: 58E05; Secondary: 35J35, 35J65.

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