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

Bonanno, Gabriele

J. Math. Anal. Appl. 299, No. 2, 600-614 (2004).

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.

MSC:

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

Keywords:

Critical point; Multiple solutions; Two-point boundary value problem; \(p\)-Laplacian

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