The concentration-compactness principle in the calculus of variations. The locally compact case. II

DOI10.1016/S0294-1449(16)30422-XzbMath0704.49004OpenAlexW2916567905MaRDI QIDQ917004

Pierre-Louis Lions

Publication date: 1984

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1984__1_4_223_0

zbMATH Keywords

Schrödinger equationsconcentration-compactness principleChoquard- Pekar problemHartree-Fock problemsminimization over manifoldsnonlinear field equationsrotating star problem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Existence theories for free problems in two or more independent variables (49J10) Existence theories for problems in abstract spaces (49J27)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• The existence of a non-minimal solution to the SU(2) Yang-Mills-Higgs equations on \(R^ 3.\) II
• Nonlinear elliptic eigenvalue problems on an infinite strip-global theory of bifurcation and asymptotic bifurcation
• Finite-amplitude steady waves in stratified fluids
• Symétrie et compacité dans les espaces de Sobolev
• Existence of solitary waves in higher dimensions
• Existence of axisymmetric equilibrium figures
• Multiple solutions of differential equations without the Palais-Smale condition
• A global theory of steady vortex rings in an ideal fluid
• Boundary value problems for a class of nonlinear differential equations
• A minimum-maximum principle for a class of non-linear integral equations
• On the existence and structure of stationary states for a nonlinear Klein-Gordon equation
• Variational solutions of some nonlinear free boundary problems
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• Nonlinear elliptic problems in strip-like domains: symmetry of positive vortex rings
• A remark on comparison results via symmetrization
• Existence d'une infinité d'ondes solitaires pour des équations de champs non linéaires dans le plan
• Some remarks on Hartree equation