Some abstract critical point theorems and applications
Anna Maria Candela - Dipartimento Di Matematica, Universita' degli Studi di Bari "Aldo Moro", 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
Received: July 2008; Revised: March 2009; Published: September 2009.