Journal ArticleDOI
Morse index of some min‐max critical points. I. Application to multiplicity results
A. Bahri,Pierre-Louis Lions +1 more
TLDR
In this paper, a resultat general sur des bornes inferieures for des indices de Morse de points critiques obtenus par des principes de min-max is presented.Abstract:
On donne un resultat general sur des bornes inferieures pour des indices de Morse de points critiques obtenus par des principes de min-max. En combinant cette information avec une inegalite semiclassique on obtient des estimations pointues sur la croissance de certaines valeurs critiques, a partir desquelles on deduit de nouveaux resultats de multiplicite pour des solutions d'equations elliptiques semi-lineaires d'ordre 2read more
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Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
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Variational Methods for Nonlocal Fractional Problems
TL;DR: A thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators can be found in this paper, where the authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of equations, plus their application to various processes arising in the applied sciences.
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On a superlinear elliptic equation
Zhi-Qiang Wang,Zhi-Qiang Wang +1 more
TL;DR: In this paper, the authors established multiple solutions for a semilinear elliptic equation with superlinear nonlinearity without assuming any symmetry, and proved that these solutions can be obtained without any assumption of symmetry.
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Selected new aspects of the calculus of variations in the large
Ivar Ekeland,Nassif Ghoussoub +1 more
TL;DR: In this paper, the authors discuss some of the recent developments in variational methods while emphasizing new applications to nonlinear problems, including the formulation of variational set-ups which provide more information on the location of critical points and therefore on the qualitative properties of the solutions of corresponding Euler-Lagrange equations.
Book
Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS
TL;DR: In this paper, a mathematical model describing electrostatic actuated MEMS is presented, which can be used as a motivational introduction to many recent methods of nonlinear analysis and PDEs through the analysis of a set of equations that have enormous practical significance.
References
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Dual variational methods in critical point theory and applications
TL;DR: In this paper, general existence theorems for critical points of a continuously differentiable functional I on a real Banach space are given for the case in which I is even.
Book
Functional integration and quantum physics
TL;DR: The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography as discussed by the authors The Basic Process Bound State problems
Journal ArticleDOI
Weak Type Estimates for Singular Values and the Number of Bound States of Schrodinger Operators
Journal ArticleDOI
A perturbation method in critical point theory and applications
Abbas Bahri,Henri Berestycki +1 more
TL;DR: In this paper, the existence and multiplicity results for nonlinear elliptic equations of the type -Au = |u|''_1u + h(x) in P», u = 0 on 3s.
Journal ArticleDOI
Bounds on the eigenvalues of the Laplace and Schroedinger operators
TL;DR: In this paper, the Laplace-Beltrami operator is replaced by a Riemannian manifold, M, where 1121 is the volume of SI and Cn = (47r)~~ r(l + njiy).