Some abstract critical point theorems and applications

Pages: 133 - 142, Issue Special, September 2009

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Anna Maria Candela - Dipartimento Di Matematica, Universita' degli Studi di Bari "Aldo Moro", via E. Orabona 4, 70125 Bari, Italy (email)
Giuliana Palmieri - Dipartimento Di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy (email)

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.

Keywords:  Critical point, Condition $(C)$, Deformation Lemma, Mountain Pass Theorem, Linking Theorem, symmetric functional, $p$--Laplacian type equation
Mathematics Subject Classification:  Primary: 58E05; Secondary: 35J35, 35J65

Received: July 2008;      Revised: March 2009;      Published: September 2009.