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Volumn 1, Issue 4, 1984, Pages 223-283

The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2

Author keywords

35 J 65; 47 H 15; 49 A 22; 49 H 05; 58 E 30; 81 C 05; concentration function; Concentration compactness principle; minimization problem; nonlinear field equations; nonlinear Schrodinger equations; rotating stars; solitary waves; unbounded domains; vortex rings

Indexed keywords

CALCULATIONS; CONTROL NONLINEARITIES; SCHRODINGER EQUATION; SOLITONS; VORTEX FLOW;

EID: 85030719142     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(16)30422-X     Document Type: Article
Times cited : (1705)

References (41)
  • 1
    • 85050664095 scopus 로고    scopus 로고
    • A remark on comparison results for solutions of second order elliptic equations via symmetrization. Preprint.
    • A. Alvino, P. L. Lions and G. Trombetti, A remark on comparison results for solutions of second order elliptic equations via symmetrization. Preprint.
    • Alvino, A.1    Lions, P.L.2    Trombetti, G.3
  • 2
    • 85050673890 scopus 로고    scopus 로고
    • Nonlinear elliptic eigenvalue problems on an infinite strip: global theory of bifurcation and asymptotic bifurcation. To appear in Math. Ann.
    • 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.
    • Amick, C.J.1    Toland, J.F.2
  • 3
    • 0017635076 scopus 로고
    • Existence of axisymmetric equilibrium figures
    • Auchmuty, J.F.G., Existence of axisymmetric equilibrium figures. Arch. Rat. Mech. Anal. t. 65 (1977), 249–261.
    • (1977) Arch. Rat. Mech. Anal. , vol.t. 65 , pp. 249-261
    • Auchmuty, J.F.G.1
  • 4
    • 0001063081 scopus 로고
    • Variational solutions of some nonlinear free boundary problems
    • Auchmuty, J.F.G., Reals, R., Variational solutions of some nonlinear free boundary problems. Arch. Rat. Mech. Anal. t. 43 (1971), 255–271.
    • (1971) Arch. Rat. Mech. Anal. , vol.t. 43 , pp. 255-271
    • Auchmuty, J.F.G.1    Reals, R.2
  • 6
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations. I. — Existence of a ground state
    • Berestycki, H., Lions, P.L., Nonlinear scalar field equations. I. — Existence of a ground state. Arch. Rat. Mech. Anal. t. 82 (1983), 313–346.
    • (1983) Arch. Rat. Mech. Anal. , vol.t. 82 , pp. 313-346
    • Berestycki, H.1    Lions, P.L.2
  • 7
    • 0000935970 scopus 로고
    • Existence d'ondes solitaires dans des problèmes non linéaires du type Klein‐Gordon
    • Berestycki, H., Lions, P.L., Existence d'ondes solitaires dans des problèmes non linéaires du type Klein‐Gordon. C. R. Acad. Sci. Paris t. 287 (1978), 503–506, t. 288, 1979, 395–398.
    • (1978) C. R. Acad. Sci. Paris , vol.t. 287 , pp. 503-506
    • Berestycki, H.1    Lions, P.L.2
  • 8
    • 0020591566 scopus 로고
    • Nonlinear scalar field equations. II. — Existence of infinitely many solutions
    • Berestycki, H., Lions, P.L., Nonlinear scalar field equations. II. — Existence of infinitely many solutions. Arch. Rat. Mech. Anal. t. 82 (1983), 347–376.
    • (1983) Arch. Rat. Mech. Anal. , vol.t. 82 , pp. 347-376
    • Berestycki, H.1    Lions, P.L.2
  • 10
    • 36248948733 scopus 로고
    • Existence d’états multiples dans des équations de champs scalaires non linéaires dans le cas de masse nulle
    • Berestycki, H., Lions, P.L., Existence d’états multiples dans des équations de champs scalaires non linéaires dans le cas de masse nulle. C. R. Acad. Sci. Paris t. 297 (1983), 267–270.
    • (1983) C. R. Acad. Sci. Paris , vol.t. 297 , pp. 267-270
    • Berestycki, H.1    Lions, P.L.2
  • 12
    • 0001240129 scopus 로고
    • On the existence and structure of stationary states for a non‐linear Klein-Gordan equation
    • Berger, M.S., On the existence and structure of stationary states for a non‐linear Klein-Gordan equation. J. Funct. Anal. t. 9 (1972), 249–261.
    • (1972) J. Funct. Anal. , vol.t. 9 , pp. 249-261
    • Berger, M.S.1
  • 13
    • 85050650830 scopus 로고    scopus 로고
    • Finite amplitude steady waves in stratified fluids. To appear in J. Math. Pures Appl.
    • J. Bona, D. K. Bose and R. E. L. Turner, Finite amplitude steady waves in stratified fluids. To appear in J. Math. Pures Appl.
    • Bona, J.1    Bose, D.K.2    Turner, R.E.L.3
  • 14
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some non‐linear Schrödinger equations
    • Cazenave, T., Lions, P.L., Orbital stability of standing waves for some non‐linear Schrödinger equations. Comm. Math. Phys. t. 85 (1982), 549–561.
    • (1982) Comm. Math. Phys. , vol.t. 85 , pp. 549-561
    • Cazenave, T.1    Lions, P.L.2
  • 15
    • 51249191299 scopus 로고
    • A minimum‐maximum principle for a class of nonlinear integral equations
    • Coffman, C.V., A minimum‐maximum principle for a class of nonlinear integral equations. J. Anal. Math. t. 22 (1969), 341–419.
    • (1969) J. Anal. Math. , vol.t. 22 , pp. 341-419
    • Coffman, C.V.1
  • 16
    • 0343766384 scopus 로고
    • On a class of nonlinear elliptic boundary value problems
    • Coffman, C.V., On a class of nonlinear elliptic boundary value problems. J. Math. Mech. t. 19 (1970), 351–356.
    • (1970) J. Math. Mech. , vol.t. 19 , pp. 351-356
    • Coffman, C.V.1
  • 17
    • 0015249887 scopus 로고
    • 3 = 0 and a variational characterization of other solutions
    • 3 = 0 and a variational characterization of other solutions. Arch. Rat. Mech. Anal. t. 46 (1972), 81–95.
    • (1972) Arch. Rat. Mech. Anal. , vol.t. 46 , pp. 81-95
    • Coffman, C.V.1
  • 18
    • 0000995516 scopus 로고
    • Action minima among solutions to a class of Euclidean scalar field equations
    • Coleman, S., Glazer, V., Martin, A., Action minima among solutions to a class of Euclidean scalar field equations. Comm. Math. Phys. t. 58 (1978), 211–221.
    • (1978) Comm. Math. Phys. , vol.t. 58 , pp. 211-221
    • Coleman, S.1    Glazer, V.2    Martin, A.3
  • 19
    • 85050683869 scopus 로고
    • Existence d'une infinité d'ondes solitaires pour des équations de champs non linéaires dans le plan
    • Esteban, M.J., Existence d'une infinité d'ondes solitaires pour des équations de champs non linéaires dans le plan. Ann. Fac. Sc. Toulouse t. II (1980), 181–191.
    • (1980) Ann. Fac. Sc. Toulouse , vol.t. II , pp. 181-191
    • Esteban, M.J.1
  • 20
    • 0000692369 scopus 로고
    • Nonlinear elliptic problems in strip‐like domains; symmetry of positive vortex rings
    • Esteban, M.J., Nonlinear elliptic problems in strip‐like domains; symmetry of positive vortex rings. Nonlinear Anal. T. M. A. t. 7 (1983), 365–379.
    • (1983) Nonlinear Anal. T. M. A. , vol.t. 7 , pp. 365-379
    • Esteban, M.J.1
  • 21
    • 34250422161 scopus 로고
    • A global theory of steady vortex rings in an ideal fluid
    • Fraenkel, L.E., Berger, M.S., A global theory of steady vortex rings in an ideal fluid. Acta Math. 132 (1974), 13–51.
    • (1974) Acta Math. , vol.132 , pp. 13-51
    • Fraenkel, L.E.1    Berger, M.S.2
  • 23
    • 0000368619 scopus 로고
    • The Hartree‐Fock theory for Coulomb systems
    • Lieb, E.H., Simon, B., The Hartree‐Fock theory for Coulomb systems. Comm. Math. Phys. t. 53 (1974), 185–194.
    • (1974) Comm. Math. Phys. , vol.t. 53 , pp. 185-194
    • Lieb, E.H.1    Simon, B.2
  • 24
    • 85030707196 scopus 로고
    • The concentration‐compactness principle in the Calculus of Variations. The locally compact case, part 1
    • Lions, P.L., 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), 109–145.
    • (1984) Ann. I. H. P. Anal. non linéaire , vol.t. 1 , pp. 109-145
    • Lions, P.L.1
  • 25
    • 84935768760 scopus 로고
    • Compactness and topological methods for some nonlinear variational problems of Mathematical Physics
    • A.R. Bishop D.K. Campbell B. Nicolaenko North‐Holland Amsterdam
    • Lions, P.L., Compactness and topological methods for some nonlinear variational problems of Mathematical Physics. Bishop, A.R., Campbell, D.K., Nicolaenko, B., (eds.) Nonlinear Problems: Present and Future, 1982, North‐Holland, Amsterdam.
    • (1982) Nonlinear Problems: Present and Future
    • Lions, P.L.1
  • 26
    • 0000296501 scopus 로고
    • Symmetry and compactness in Sobolev spaces
    • Lions, P.L., Symmetry and compactness in Sobolev spaces. J. Funct. Anal. t. 49 (1982), 315–334.
    • (1982) J. Funct. Anal. , vol.t. 49 , pp. 315-334
    • Lions, P.L.1
  • 27
    • 4744340433 scopus 로고
    • Principe de concentration‐compacité en Calcul des Variations
    • Lions, P.L., Principe de concentration‐compacité en Calcul des Variations. C. R. Acad. Sci. Paris t. 294 (1982), 261–264.
    • (1982) C. R. Acad. Sci. Paris , vol.t. 294 , pp. 261-264
    • Lions, P.L.1
  • 29
    • 0141672305 scopus 로고
    • Some remarks on Hartree equations
    • Lions, P.L., Some remarks on Hartree equations. Nonlinear Anal. T. M. A. t. 5 (1981), 1245–1256.
    • (1981) Nonlinear Anal. T. M. A. , vol.t. 5 , pp. 1245-1256
    • Lions, P.L.1
  • 31
    • 85050654631 scopus 로고    scopus 로고
    • The concentration‐compactness principle in the Calculus of Variations. The limit case. To appear in Revista Matematica Iberoamericana.
    • P. L. Lions, The concentration‐compactness principle in the Calculus of Variations. The limit case. To appear in Revista Matematica Iberoamericana.
    • Lions, P.L.1
  • 32
    • 84974345814 scopus 로고
    • La méthode de concentration‐compacité en Calcul des Variations
    • École Polytechnique Palaiseau
    • Lions, P.L., La méthode de concentration‐compacité en Calcul des Variations. Séminaire Goulaouic‐Meyer‐Schwartz, 1982‐1983, 1983, École Polytechnique, Palaiseau.
    • (1983) Séminaire Goulaouic‐Meyer‐Schwartz, 1982‐1983
    • Lions, P.L.1
  • 33
    • 0007031446 scopus 로고
    • Applications de la méthode de concentration‐compacité à l'existence de fonctions extrêmales
    • Lions, P.L., Applications de la méthode de concentration‐compacité à l'existence de fonctions extrêmales. C. R. Acad. Sci. Paris t. 296 (1983), 645–648.
    • (1983) C. R. Acad. Sci. Paris , vol.t. 296 , pp. 645-648
    • Lions, P.L.1
  • 34
    • 0011603301 scopus 로고
    • On a nonlinear differential equation arising in Nuclear physics
    • Nehari, Z., On a nonlinear differential equation arising in Nuclear physics. Proc. R. Irish Acad. t. 62 (1963), 117–135.
    • (1963) Proc. R. Irish Acad. , vol.t. 62 , pp. 117-135
    • Nehari, Z.1
  • 35
    • 0000514956 scopus 로고
    • Eigenfunctions of the equation Δu + λf(u) = 0
    • Pohozaev, S., Eigenfunctions of the equation Δu + λf(u) = 0. Soviet Math. Dokl. t. 165 (1965), 1408–1412.
    • (1965) Soviet Math. Dokl. , vol.t. 165 , pp. 1408-1412
    • Pohozaev, S.1
  • 36
    • 84972500113 scopus 로고
    • Boundary value problems for a class of nonlinear differential equations
    • Ryder, G.H., Boundary value problems for a class of nonlinear differential equations. Pac. J. Math. t. 22 (1967), 477–503.
    • (1967) Pac. J. Math. , vol.t. 22 , pp. 477-503
    • Ryder, G.H.1
  • 37
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher dimensions
    • Strauss, W., Existence of solitary waves in higher dimensions. Comm. Math. Phys. t. 55 (1977), 149–162.
    • (1977) Comm. Math. Phys. , vol.t. 55 , pp. 149-162
    • Strauss, W.1
  • 38
    • 0010601361 scopus 로고
    • Multiple solutions of differential equations without the Palais‐Smale condition
    • Struwe, M., Multiple solutions of differential equations without the Palais‐Smale condition. Math. Ann. t. 261 (1982), 399–412.
    • (1982) Math. Ann. , vol.t. 261 , pp. 399-412
    • Struwe, M.1
  • 39
    • 85050686315 scopus 로고    scopus 로고
    • Self‐focusing of very powerful laser beams. U. S. Dept of Commerce. N. B. S. Special Publication 387.
    • B. R. Suydam, Self‐focusing of very powerful laser beams. U. S. Dept of Commerce. N. B. S. Special Publication 387.
    • Suydam, B.R.1
  • 40
    • 0000253928 scopus 로고
    • Elliptic equations and rearrangements
    • Talenti, G., Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa t. 3 (1976), 697–718.
    • (1976) Ann. Scuola Norm. Sup. Pisa , vol.t. 3 , pp. 697-718
    • Talenti, G.1


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