@article{AIHPC_1984__1_2_109_0, author = {Lions, P. L.}, title = {The concentration-compactness principle in the calculus of variations. {The} locally compact case, part 1}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {109--145}, publisher = {Gauthier-Villars}, volume = {1}, number = {2}, year = {1984}, mrnumber = {778970}, zbl = {0541.49009}, language = {en}, url = {http://www.numdam.org/item/AIHPC_1984__1_2_109_0/} }
TY - JOUR AU - Lions, P. L. TI - The concentration-compactness principle in the calculus of variations. The locally compact case, part 1 JO - Annales de l'I.H.P. Analyse non linéaire PY - 1984 SP - 109 EP - 145 VL - 1 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1984__1_2_109_0/ LA - en ID - AIHPC_1984__1_2_109_0 ER -
%0 Journal Article %A Lions, P. L. %T The concentration-compactness principle in the calculus of variations. The locally compact case, part 1 %J Annales de l'I.H.P. Analyse non linéaire %D 1984 %P 109-145 %V 1 %N 2 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_1984__1_2_109_0/ %G en %F AIHPC_1984__1_2_109_0
Lions, P. L. The concentration-compactness principle in the calculus of variations. The locally compact case, part 1. Annales de l'I.H.P. Analyse non linéaire, Tome 1 (1984) no. 2, pp. 109-145. http://www.numdam.org/item/AIHPC_1984__1_2_109_0/
[1] Variational solutions of some nonlinear free boundary problems. Arch. Rat. Mech. Anal., t. 43, 1971, p. 255-271. | MR | Zbl
and ,[2] Models of rotating stars. Astrophys. J., t. 165, 1971, p. 79-82.
and ,[3] Nonlinear scalar field equations. I. Existence of a ground state. Arch. Rat. Mech. Anal., t. 82, 1983, p. 313-346. | MR | Zbl
and ,[4] Nonlinear scalar field equations. II. Existence of infinitely many solutions. Arch. Rat. Mech. Anal., t. 82, 1983, p. 347-376. | MR | Zbl
and ,[5]
and , in preparation.[6] On the existence and structure of stationary states for a nonlinear Klein-Gordon equation. J. Funct. Anal., t. 9, 1972, p. 249-261. | MR | Zbl
,[7] Orbital stability of standing waves for some nonlinear Schrödinger equations. Comm. Math. Phys., t. 85, 1982, p. 549-561. | MR | Zbl
and ,[8] Uniqueness of the ground state solution for Δu - u + u3 = 0 and a variational characterization of other solutions. Arch. Rat. Mech. Anal., t. 46, 1972, p. 81-95. | MR | Zbl
,[9] Action minima among solutions to a class of Euclidean scalar field equations. Comm. Math. Phys., t. 58, 1978, p. 211-221. | MR
, and ,[10] personal communication.
and ,[11] Existence and non-existence results for semilinear elliptic problems in unbounded domains. Proc. Roy. Edim., t. 93 A, 1982, p. 1-14. | MR | Zbl
and ,[12] A global theory of steady vortex rings in an ideal fluid. Acta Math., t. 132, 1974, p. 13-51. | MR | Zbl
and ,[13] Variational principles and free-boundary problems, Wiley, New York, 1982. | MR | Zbl
,[14] Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris, 1954. | JFM | Zbl
,[15] Existence and uniqueness of the minimizing solutions of Choquard's nonlinear equation. Stud. Appl. Math., t. 57, 1977, p. 93-105. | MR | Zbl
,[16] Minimization problems in L1(R3). J. Funct. Anal., t. 41, 1981, p. 236-275. | MR | Zbl
,[17] Compactness and topological methods for some nonlinear variational problems of Mathematical Physics. In Nonlinear Problems : Present and Future ; A. R. Bishop, D. K. Campbell, B. Nicolaenko (eds.), North-Holland, Amsterdam, 1982. | MR | Zbl
,[18] Symmetry and compactness in Sobolev spaces. J. Funct. Anal., t. 49, 1982, p. 315-334. | MR | Zbl
,[19] Principe de concentration-compacité en Calcul des Variations. C. R. Acad. Sci. Paris, t. 294, 1982, p. 261-264. | MR | Zbl
,[20] On the concentration-compactness principle. In Contributions to Non-linear Partial Differential Equations. Pitman, London, 1983. | MR | Zbl
,[21] The Choquard equation and related questions. Nonlinear Anal. T. M. A., t. 4, 1980, p. 1063-1073. | MR | Zbl
,[22] On a nonlinear differential equation arising in nuclear physics. Proc. R. Irish Acad., t. 62, 1963, p. 117-135. | MR | Zbl
,[23] Probability measures on metric spaces, Academic Press, New York, 1967. | MR | Zbl
,[24] Boundary value problems for a class of nonlinear differential equations. Pac. J. Math., t. 22, 1967, p. 477-503. | MR | Zbl
,[25] Existence of solitary waves in higher dimensions. Comm. Math. Phys., t. 55, 1977, p. 149-162. | MR | Zbl
,[26] Self-focusing of very powerful laser beams. U. S. Dept. of Commerce. N. B. S. Special Publication 387.
,