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2009, 2009(Special): 133-142. doi: 10.3934/proc.2009.2009.133

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, Italy
2. 

Dipartimento Di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy

Received  July 2008 Revised  March 2009 Published  September 2009

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.
Keywords: Critical point, $p$--Laplacian type equation, Deformation Lemma, symmetric functional, Mountain Pass Theorem, Linking Theorem, Condition $(C)$.
Mathematics Subject Classification: Primary: 58E05; Secondary: 35J35, 35J65.
Citation: Anna Maria Candela, Giuliana Palmieri. Some abstract critical point theorems and applications. Conference Publications, 2009, 2009 (Special) : 133-142. doi: 10.3934/proc.2009.2009.133
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