@article{AIHPC_1984__1_4_223_0, author = {Lions, Pierre-Louis}, title = {The concentration-compactness principle in the calculus of variations. The locally compact case, part 2}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {223--283}, publisher = {Gauthier-Villars}, volume = {1}, number = {4}, year = {1984}, zbl = {0704.49004}, mrnumber = {778974}, language = {en}, url = {www.numdam.org/item/AIHPC_1984__1_4_223_0/} }
Lions, P. L. The concentration-compactness principle in the calculus of variations. The locally compact case, part 2. Annales de l'I.H.P. Analyse non linéaire, Tome 1 (1984) no. 4, pp. 223-283. http://www.numdam.org/item/AIHPC_1984__1_4_223_0/
[1] A remark on comparison results for solutions of second order elliptic equations via symmetrization. Preprint.
, and ,[2] Nonlinear elliptic eigenvalue problems on an infinite strip: global theory of bifurcation and asymptotic bifurcation. To appear in Math. Ann. | MR 692860 | Zbl 0489.35067
and ,[3] Existence of axisymmetric equilibrium figures. Arch. Rat. Mech. Anal., t. 65, 1977, p. 249-261. | MR 446076 | Zbl 0366.76083
,[4] Variational solutions of some nonlinear free boundary problems. Arch. Rat. Mech. Anal., t. 43, 1971, p. 255-271. | MR 337260 | Zbl 0225.49013
and ,[5] work in preparation.
, and ,[6] Nonlinear scalar field equations. I. - Existence of a ground state. Arch. Rat. Mech. Anal., t. 82, 1983, p. 313-346. | MR 695535 | Zbl 0533.35029
and ,[7] Existence d'ondes solitaires dans des problèmes non linéaires du type Klein-Gordon. C. R. Acad. Sci. Paris, t. 287, 1978, p. 503-506; t. 288, 1979, p. 395-398. | Zbl 0391.35055
and ,[8] Nonlinear scalar field equations. II. - Existence of infinitely many solutions. Arch. Rat. Mech. Anal., t. 82, 1983, p. 347-376. | MR 695536 | Zbl 0556.35046
and ,[9] Existence of stationary states in Nonlinear scalar field equations. In Bifurcation Phenomena in Mathematical Physics and related topics, C. Bardos and D. Bessis (eds.), Reidel, Dordrecht, 1980.
and ,[10] Existence d'états multiples dans des equations de champs scalaires non linéaires dans le cas de masse nulle. C. R. Acad. Sci. Paris, t. 297, 1983, p. 267-270. | MR 727185 | Zbl 0542.35072
and ,[11] work in preparation.
and ,[12] On the existence and structure of stationary states for a non-linear Klein-Gordon equation. J. Funct. Anal., t. 9, 1972, p. 249-261. | MR 299966 | Zbl 0224.35061
,[13] Finite amplitude steady waves in stratified fluids. To appear in J. Math. Pures Appl. | MR 735931 | Zbl 0491.35049
, and ,[14] Orbital stability of standing waves for some non-linear Schrödinger equations. Comm. Math. Phys., t. 85, 1982, p. 549-561. | MR 677997 | Zbl 0513.35007
and ,[15] A minimum-maximum principle for a class of nonlinear integral equations. J. Anal. Math., t. 22, 1969, p. 391-419. | MR 249983 | Zbl 0179.15601
,[16] On a class of nonlinear elliptic boundary value problems. J. Math. Mech., t. 19, 1970, p. 351-356. | Zbl 0194.42103
,[17] 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 333489 | Zbl 0249.35029
,[18] Action minima among solutions to a class of Euclidean scalar field equations. Comm. Math. Phys., t. 58, 1978, p. 211-221. | MR 468913
, and ,[19] Existence d'une infinité d'ondes solitaires pour des équations de champs non linéaires dans le plan. Ann. Fac. Sc. Toulouse, t. II, 1980, p. 181- 191. | Numdam | MR 614011 | Zbl 0458.35040
,[20] Nonlinear elliptic problems in strip-like domains; symmetry of positive vortex rings. Nonlinear Anal. T. M. A., t. 7, 1983, p. 365-379. | MR 696736 | Zbl 0513.35035
,[21] A global theory of steady vortex rings in an ideal fluid. Acta Math., 132, 1974, p. 13-51. | MR 422916 | Zbl 0282.76014
and ,[22] Symmetry of positive solutions of non-linear elliptic equations in Rn. In Math. Anal. Appl., part 1, L. Nachbin (ed.), Academic Press, 1981.
, and ,[23] The Hartree-Fock theory for Coulomb systems. Comm. Math. Phys., t. 53, 1974, p. 185-194. | MR 452286
and ,[24] The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. Ann. I. H. P. Anal. non linéaire, t. 1, 1984, p. 109-145. | Numdam | MR 778970 | Zbl 0541.49009
,[25] 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 675625 | Zbl 0496.35079
,[26] Symmetry and compactness in Sobolev spaces. J. Funct. Anal., t. 49, 1982, p. 315-334. | MR 683027 | Zbl 0501.46032
,[27] Principe de concentration-compacité en Calcul des Variations. C. R. Acad. Sci. Paris, t. 294, 1982, p. 261-264. | MR 653747 | Zbl 0485.49005
,[28] On the concentration-compactness principle. In Contributions to Nonlinear Partial Differential Equations, Pitman, London, 1983. | MR 730813 | Zbl 0522.49007
,[29] Some remarks on Hartree equations. Nonlinear Anal. T. M. A., t. 5, 1981, p. 1245-1256. | MR 636734 | Zbl 0472.35074
,[30] Minimization problems in L1(RN). J. Funct. Anal., t. 49, 1982, p. 315-334.
,[31] The concentration-compactness principle in the Calculus of Variations. The limit case. To appear in Revista Matematica Iberoamericana. | MR 730813 | Zbl 0704.49005
,[32] La méthode de concentration-compacité en Calcul des Variations. In Séminaire Goulaouic-Meyer-Schwartz, 1982-1983, École Polytechnique, Palaiseau, 1983. | Numdam | MR 716902
,[33] Applications de la méthode de concentration-compacité à l'existence de fonctions extrêmales. C. R. Acad. Sci. Paris, t. 296, 1983, p. 645-648. | MR 705681 | Zbl 0522.49008
,[34] On a nonlinear differential equation arising in Nuclear physics. Proc. R. Irish Acad., t. 62, 1963, p. 117-135. | MR 165176 | Zbl 0124.30204
,[35] Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl., t. 165, 1965, p. 1408-1412. | MR 192184 | Zbl 0141.30202
,[36] Boundary value problems for a class of nonlinear differential equations. Pac. J. Math., t. 22, 1967, p. 477-503. | MR 219794 | Zbl 0152.28303
,[37] Existence of solitary waves in higher dimensions. Comm. Math. Phys., t. 55, 1977, p. 149-162. | MR 454365 | Zbl 0356.35028
,[38] Multiple solutions of differential equations without the Palais-Smale condition. Math. Ann., t. 261, 1982, p. 399-412. | MR 679798 | Zbl 0506.35034
,[39] Self-focusing of very powerful laser beams. U. S. Dept of Commerce. N. B. S. Special Publication 387.
,[40] Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa, t. 3, 1976, p. 697-718. | Numdam | MR 601601 | Zbl 0341.35031
,[41] The existence of a non-minimal solution to the SU(2) Yang-Mills-Hoggs equations on R3. Comm. Math. Phys., t. 86, 1982, p. 257 ; t. 86, 1982, p. 299. | Zbl 0514.58016
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