메뉴 건너뛰기




Volumn 16, Issue 6, 2009, Pages 681-715

Stationary solutions for the non-linear Hartree equation with a slowly varying potential

Author keywords

Elliptic equation; Shadowing lemma

Indexed keywords


EID: 76549109293     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-009-0030-0     Document Type: Article
Times cited : (9)

References (18)
  • 1
    • 6344263972 scopus 로고    scopus 로고
    • On a periodic Schrödinger equation with nonlocal superlinear part
    • Ackermann N.: On a periodic Schrödinger equation with nonlocal superlinear part. Math. Z. 248(2), 423-443 (2004).
    • (2004) Math. Z. , vol.248 , Issue.2 , pp. 423-443
    • Ackermann, N.1
  • 3
    • 0039679600 scopus 로고
    • The shadowing lemma for elliptic PDE
    • (Lisbon), NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci. vol. 37. Springer, Berlin (1987)
    • Angenent, S.: The shadowing lemma for elliptic PDE. Dynamics of infinite- dimensional systems (Lisbon, 1986), pp. 7-22. NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci. vol. 37. Springer, Berlin (1987).
    • (1986) Dynamics of infinite- dimensional systems , pp. 7-22
    • Angenent, S.1
  • 4
    • 33747045188 scopus 로고    scopus 로고
    • Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations
    • Cingolani S., Nolasco M.: Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations. Proc. R. Soc. Edinburgh 128 A, 1249-1260 (1998).
    • (1998) Proc. R. Soc. Edinburgh , vol.128 A , pp. 1249-1260
    • Cingolani, S.1    Nolasco, M.2
  • 5
    • 79551496714 scopus 로고    scopus 로고
    • Derivation of the nonlinear Schrödinger equation from a many-body Coulomb system
    • Erdös L., Yau H.-T.: Derivation of the nonlinear Schrödinger equation from a many-body Coulomb system. Adv. Theor. Math. Phys. 5, 1169-1205 (2001).
    • (2001) Adv. Theor. Math. Phys. , vol.5 , pp. 1169-1205
    • Erdös, L.1    Yau, H.-T.2
  • 6
    • 0001613187 scopus 로고
    • Nonspreading wave packets for the cubic schrödinger equation with a bounded potential
    • Floer A., Weinstein A.: Nonspreading wave packets for the cubic schrödinger equation with a bounded potential. J. Funct. Anal. 69, 397-408 (1986).
    • (1986) J. Funct. Anal. , vol.69 , pp. 397-408
    • Floer, A.1    Weinstein, A.2
  • 9
    • 79959209052 scopus 로고    scopus 로고
    • Mean-field limit of quantum bose gases and nonlinear hartree equation
    • Exp. No. XIX, cole Polytech., Palaiseau
    • Fröhlich, J., Lenzmann, E.: Mean-field limit of quantum bose gases and nonlinear hartree equation. Seminaire equations aux Drives Partielles. Exp. No. XIX, cole Polytech., Palaiseau (2004).
    • (2004) Seminaire equations aux Drives Partielles
    • Fröhlich, J.1    Lenzmann, E.2
  • 10
    • 0036101479 scopus 로고    scopus 로고
    • On the point-particle (Newtonian) limit of the non-linear Hartree equation
    • Fröhlich J., Tsai T.-P., Yau H.-T.: On the point-particle (Newtonian) limit of the non-linear Hartree equation. Commun. Math. Phys. 225, 223-274 (2002).
    • (2002) Commun. Math. Phys. , vol.225 , pp. 223-274
    • Fröhlich, J.1    Tsai, T.-P.2    Yau, H.-T.3
  • 12
    • 33846791634 scopus 로고
    • The classical limit for quantum mechanical correlation functions
    • Hepp K.: The classical limit for quantum mechanical correlation functions. Commun. Math. Phys. 35, 265-277 (1974).
    • (1974) Commun. Math. Phys. , vol.35 , pp. 265-277
    • Hepp, K.1
  • 13
    • 84916181784 scopus 로고
    • Existence and Uniqueness of the minimizing solution of Choquard's nonlinear equation
    • Lieb E. H.: Existence and Uniqueness of the minimizing solution of Choquard's nonlinear equation. Stud. Appl. Math. 57, 93-105 (1977).
    • (1977) Stud. Appl. Math. , vol.57 , pp. 93-105
    • Lieb, E.H.1
  • 14
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case I
    • Lions P.-L.: The concentration-compactness principle in the calculus of variations. The locally compact case I. Ann. Inst. Poincaré Anal. Non Linéaire 1, 109-145 (1984).
    • (1984) Ann. Inst. Poincaré Anal. Non Linéaire , vol.1 , pp. 109-145
    • Lions, P.-L.1
  • 15
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case II
    • Lions P.-L.: The concentration-compactness principle in the calculus of variations. The locally compact case II. Ann. Inst. Poincaré Anal. Non Linéaire 1, 223-283 (1984).
    • (1984) Ann. Inst. Poincaré Anal. Non Linéaire , vol.1 , pp. 223-283
    • Lions, P.-L.1
  • 16
    • 0000998584 scopus 로고
    • On positive multi-bump states of nonlinear Schrödinger equation under multiple well potentials
    • Oh Y. G.: On positive multi-bump states of nonlinear Schrödinger equation under multiple well potentials. Commun. Math. Phys. 131, 223-253 (1990).
    • (1990) Commun. Math. Phys. , vol.131 , pp. 223-253
    • Oh, Y.G.1
  • 17
    • 35949020007 scopus 로고
    • Kinetic equations from Hamiltonian dynamics
    • Spohn H.: Kinetic equations from Hamiltonian dynamics. Rev. Mod. Phys. 52(3), 569-615 (1980).
    • (1980) Rev. Mod. Phys. , vol.52 , Issue.3 , pp. 569-615
    • Spohn, H.1
  • 18
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • Weinstein M. I.: Modulational stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 16, 472-491 (1985).
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 472-491
    • Weinstein, M.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.