منابع مشابه
Geometric 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 Theorem for a Suitable Class of Functions
The main purpose of this paper is to establish a three critical points result without assuming the coercivity of the involved functional. To this end, a mountain-pass theorem, where the usual Palais-Smale condition is not requested, is presented. These results are then applied to prove the existence of three solutions for a two-point boundary value problem with no asymptotic conditions.
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 کاملThe 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 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: Journal of Differential Equations
سال: 1985
ISSN: 0022-0396
DOI: 10.1016/0022-0396(85)90125-1