Multiple critical points theorems without the Palais–Smale condition. (English) Zbl 1071.34015

Summary: Multiple critical points theorems, where the Palais-Smale condition on the functional is not requested, are presented. As an application, multiple solutions for a quasilinear two-point boundary value problem involving the one-dimensional \(p\)-Laplacian are obtained.


34B15 Nonlinear boundary value problems for ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
47J30 Variational methods involving nonlinear operators
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