The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 4, pp. 223-283.
@article{AIHPC_1984__1_4_223_0,
     author = {Lions, P. L.},
     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 = {http://www.numdam.org/item/AIHPC_1984__1_4_223_0/}
}
TY  - JOUR
AU  - Lions, P. L.
TI  - The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1984
DA  - 1984///
SP  - 223
EP  - 283
VL  - 1
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1984__1_4_223_0/
UR  - https://zbmath.org/?q=an%3A0704.49004
UR  - https://www.ams.org/mathscinet-getitem?mr=778974
LA  - en
ID  - AIHPC_1984__1_4_223_0
ER  - 
%0 Journal Article
%A Lions, P. L.
%T The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
%J Annales de l'I.H.P. Analyse non linéaire
%D 1984
%P 223-283
%V 1
%N 4
%I Gauthier-Villars
%G en
%F 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, Volume 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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

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

[27] P.L. Lions, Principe de concentration-compacité en Calcul des Variations. C. R. Acad. Sci. Paris, t. 294, 1982, p. 261-264. | MR | Zbl

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

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

[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 | Zbl

[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

[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 | Zbl

[34] Z. Nehari, On a nonlinear differential equation arising in Nuclear physics. Proc. R. Irish Acad., t. 62, 1963, p. 117-135. | MR | Zbl

[35] S. Pohozaev, Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl., t. 165, 1965, p. 1408-1412. | MR | Zbl

[36] G.H. Ryder, Boundary value problems for a class of nonlinear differential equations. Pac. J. Math., t. 22, 1967, p. 477-503. | MR | Zbl

[37] W. Strauss, Existence of solitary waves in higher dimensions. Comm. Math. Phys., t. 55, 1977, p. 149-162. | MR | Zbl

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

[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 | Zbl

[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