no. 4
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. 
@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. Alvino, P.L. Lions and G. Trombetti, A remark on comparison results for solutions of second order elliptic equations via symmetrization. Preprint.

[2] C.J. Amick and J.F. Toland, 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

[3] J.F.G. Auchmuty, Existence of axisymmetric equilibrium figures. Arch. Rat. Mech. Anal., t. 65, 1977, p. 249-261. | MR 446076 | Zbl 0366.76083

[4] J.F.G. Auchmuty and R. Reals, Variational solutions of some nonlinear free boundary problems. Arch. Rat. Mech. Anal., t. 43, 1971, p. 255-271. | MR 337260 | Zbl 0225.49013

[5] H. Berestycki, T. Gallouet and O. Kavian, work in preparation.

[6] H. Berestycki and P.L. Lions, 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

[7] H. Berestycki and P.L. Lions, 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

[8] H. Berestycki and P.L. Lions, 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

[9] H. Berestycki and P.L. Lions, 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.

[10] H. Berestycki and P.L. Lions, 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

[11] H. Berestycki and P.L. Lions, work in preparation.

[12] M.S. Berger, 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] J. Bona, D.K. Bose and R.E.L. Turner, Finite amplitude steady waves in stratified fluids. To appear in J. Math. Pures Appl. | MR 735931 | Zbl 0491.35049

[14] T. Cazenave and P.L. Lions, 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

[15] C.V. Coffman, 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] C.V. Coffman, On a class of nonlinear elliptic boundary value problems. J. Math. Mech., t. 19, 1970, p. 351-356. | Zbl 0194.42103

[17] C.V. Coffman, 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] S. Coleman, V. Glazer and A. Martin, Action minima among solutions to a class of Euclidean scalar field equations. Comm. Math. Phys., t. 58, 1978, p. 211-221. | MR 468913

[19] M.J. Esteban, 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] M.J. Esteban, 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] L.E. Fraenkel and M.S. Berger, A global theory of steady vortex rings in an ideal fluid. Acta Math., 132, 1974, p. 13-51. | MR 422916 | Zbl 0282.76014

[22] B. Gidas, W.N. Ni and L. Nirenberg, Symmetry of positive solutions of non-linear elliptic equations in Rn. In Math. Anal. Appl., part 1, L. Nachbin (ed.), Academic Press, 1981.

[23] E.H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems. Comm. Math. Phys., t. 53, 1974, p. 185-194. | MR 452286

[24] P.L. Lions, 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] P.L. Lions, 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] P.L. Lions, Symmetry and compactness in Sobolev spaces. J. Funct. Anal., t. 49, 1982, p. 315-334. | MR 683027 | Zbl 0501.46032

[27] P.L. Lions, 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] P.L. Lions, On the concentration-compactness principle. In Contributions to Nonlinear Partial Differential Equations, Pitman, London, 1983. | MR 730813 | Zbl 0522.49007

[29] P.L. Lions, Some remarks on Hartree equations. Nonlinear Anal. T. M. A., t. 5, 1981, p. 1245-1256. | MR 636734 | Zbl 0472.35074

[30] P.L. Lions, Minimization problems in L1(RN). J. Funct. Anal., t. 49, 1982, p. 315-334.

[31] P.L. Lions, The concentration-compactness principle in the Calculus of Variations. The limit case. To appear in Revista Matematica Iberoamericana. | MR 730813 | Zbl 0704.49005

[32] P.L. Lions, La méthode de concentration-compacité en Calcul des Variations. In Séminaire Goulaouic-Meyer-Schwartz, 1982-1983, École Polytechnique, Palaiseau, 1983. | Numdam | MR 716902

[33] P.L. Lions, 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] Z. Nehari, 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] S. Pohozaev, Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl., t. 165, 1965, p. 1408-1412. | MR 192184 | Zbl 0141.30202

[36] G.H. Ryder, 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] W. Strauss, Existence of solitary waves in higher dimensions. Comm. Math. Phys., t. 55, 1977, p. 149-162. | MR 454365 | Zbl 0356.35028

[38] M. Struwe, Multiple solutions of differential equations without the Palais-Smale condition. Math. Ann., t. 261, 1982, p. 399-412. | MR 679798 | Zbl 0506.35034

[39] B.R. Suydam, Self-focusing of very powerful laser beams. U. S. Dept of Commerce. N. B. S. Special Publication 387.

[40] G. Talenti, Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa, t. 3, 1976, p. 697-718. | Numdam | MR 601601 | Zbl 0341.35031

[41] C. Taubes, 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