Article Contents
Article Contents

Some abstract critical point theorems and applications

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

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