منابع مشابه
The intrinsic mountain pass principle
{ In this note we present a general mountain pass principle dropping any smoothness or even continuity assumptions on the functional. As a corollary, we prove existence of a point with an arbitrarily xed small slope if the "low" part of the "barrier" is suuciently far from the "boundary", obtaining in addition estimates for the location of the point.
متن کاملGeometric Analysis and the Mountain Pass Theorem
These notes are designed to serve as a template of a LaTeX article. In the process we will describe some notions of Geometric Analysis pertaining to the Mountain Pass Theorem. Little attempt was made to be a publishable set of notes, but instead to provide examples of commonly used commands, environments, and symbols in LaTeX.
متن کاملA Mountain Pass for Reacting Molecules
In this paper, we consider a neutral molecule that possesses two distinct stable positions for its nuclei, and look for a mountain pass point between the two minima in the non-relativistic Schrödinger framework. We first prove some properties concerning the spectrum and the eigenstates of a molecule that splits into pieces, a behaviour which is observed when the Palais-Smale sequences obtained ...
متن کاملCylinder Buckling: The Mountain Pass as an Organizing Center
We revisit the classical problem of the buckling of a long thin axially compressed cylindrical shell. By examining the energy landscape of the perfect cylinder, we deduce an estimate of the sensitivity of the shell to imperfections. Key to obtaining this estimate is the existence of a mountain pass point for the system. We prove the existence on bounded domains of such solutions for almost all ...
متن کاملLocating Cerami Sequences in a Mountain Pass Geometry
Let X be a real Banach space and Φ ∈ C 1 (X, R) a function with a mountain pass geometry. This ensures the existence of a Palais-Smale, and even a Cerami, sequence {u n } of approximate critical points for the mountain pass level. We obtain information about the location of such a sequence by estimating the distance of u n from S for certain types of set S as n → ∞. Under our hypotheses we can ...
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ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 1998
ISSN: 1230-3429
DOI: 10.12775/tmna.1998.044