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.

Some abstract critical point theorems and applications

CANDELA, Anna Maria;
2009

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.
978-1-60133-011-6
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/17909
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