Differential and Integral Equations

A characterization of the mountain pass geometry for functionals bounded from below

Gabriele Bonanno

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In this paper it is proved that, when a regular functional is bounded from below, the mountain pass geometry and the existence of at least two distinct local minima are equivalent conditions. As a consequence, the classical mountain pass theorem, under the additional assumption of boundedness from below of the functional, ensures actually three distinct critical points. Moreover, as application, the existence of three solutions to Hamiltonian systems is established.

Article information

Differential Integral Equations, Volume 25, Number 11/12 (2012), 1135-1142.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 34C25: Periodic solutions 34B15: Nonlinear boundary value problems


Bonanno, Gabriele. A characterization of the mountain pass geometry for functionals bounded from below. Differential Integral Equations 25 (2012), no. 11/12, 1135--1142. https://projecteuclid.org/euclid.die/1356012254

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