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Volumn 14, Issue 1, 2012, Pages

Ground and bound states for a static schrödinger poissonslater problem

Author keywords

concentration compactness; Pohozaev identity; Schr dingerPoissonSlater problem; variational methods

Indexed keywords


EID: 84857872076     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199712500034     Document Type: Article
Times cited : (70)

References (40)
  • 1
    • 12844261727 scopus 로고    scopus 로고
    • Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
    • A. Ambrosetti, V. Felli and A. Malchiodi, Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. Eur. Math. Soc. (JEMS) 7 (2005) 117-144. (Pubitemid 40167001)
    • (2005) Journal of the European Mathematical Society , vol.7 , Issue.1 , pp. 117-144
    • Ambrosetti, A.1    Felli, V.2    Malchiodi, A.3
  • 3
    • 33748570781 scopus 로고    scopus 로고
    • Bound states of nonlinear schrödinger equations with potentials vanishing at infinity
    • DOI 10.1007/BF02790279
    • A. Ambrosetti, A. Malchiodi and D. Ruiz, Bound states of nonlinear Schrödinger equations with potential vanishing at infinity, J. Anal. Math. 98 (2006) 317-348. (Pubitemid 44369827)
    • (2006) Journal d'Analyse Mathematique , vol.98 , pp. 317-348
    • Ambrosetti, A.1    Malchiodi, A.2    Ruiez, D.3
  • 4
    • 34548350707 scopus 로고
    • Dual variational methods in critical point theory and applications
    • A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973) 349-381.
    • (1973) J. Funct. Anal. , vol.14 , pp. 349-381
    • Ambrosetti, A.1    Rabinowitz, P.H.2
  • 5
    • 44649114515 scopus 로고    scopus 로고
    • Multiple bound states for the Schrödinger-Poisson problem
    • A. Ambrosetti and D. Ruiz, Multiple bound states for the Schrödinger-Poisson problem, Commun. Contemp. Math. 10 (2008) 391-404.
    • (2008) Commun. Contemp. Math. , vol.10 , pp. 391-404
    • Ambrosetti, A.1    Ruiz, D.2
  • 6
    • 0001036379 scopus 로고    scopus 로고
    • An eigenvalue problem for the Schrödinger-Maxwell equations
    • V. Benci and D. Fortunato, An eigenvalue problem for the Schrödinger-Maxwell equations, Topol. Methods Nonlinear Anal. 11 (1998) 283-293.
    • (1998) Topol. Methods Nonlinear Anal. , vol.11 , pp. 283-293
    • Benci, V.1    Fortunato, D.2
  • 7
  • 8
    • 0344494858 scopus 로고    scopus 로고
    • On an exchange interaction model for quantum transport: The Schrödinger-Poisson-Slater system
    • DOI 10.1142/S0218202503002969
    • O. Bokanowski, J. L. López and J. Soler, On an exchange interaction model for the quantum transport; the Schrödinger-Poisson-Slater term, Math. Models Methods Appl. Sci. 13 (2003) 1397-1412. (Pubitemid 37469834)
    • (2003) Mathematical Models and Methods in Applied Sciences , vol.13 , Issue.10 , pp. 1397-1412
    • Bokanowski, O.1    Lopez, J.L.2    Soler, J.3
  • 9
    • 0033409439 scopus 로고    scopus 로고
    • Local approximation of the Hartree-Fock exchange potential: A deformation approach
    • O. Bokanowski and N. J. Mauser, Local approximation of the Hartree-Fock exchange potential: A deformation approach, Math. Models Methods Appl. Sci. 9 (1999) 941-961.
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , pp. 941-961
    • Bokanowski, O.1    Mauser, N.J.2
  • 10
    • 77949423891 scopus 로고    scopus 로고
    • Ground states for the nonlinear Schrödinger equation with potentials vanishing at infinity
    • D. Bonheure and J. V. Schaftingen, Ground states for the nonlinear Schrödinger equation with potentials vanishing at infinity, to appear in Ann. Mat. Pura Appl.
    • Ann. Mat. Pura Appl
    • Bonheure, D.1    Schaftingen, J.V.2
  • 11
    • 54749148789 scopus 로고    scopus 로고
    • A Kohn-Sham system at zero temperature
    • doi:10.1088/1751-8113/41/38/385304
    • H. Cornean, K. Hoke, H. Neidhardt, P. N. Racec and J. Rehberg, A Kohn-Sham system at zero temperature, J. Phys. A 41 (2008) 385304; doi:10.1088/1751-8113/41/38/385304.
    • (2008) J. Phys. A , vol.41 , pp. 385304
    • Cornean, H.1    Hoke, K.2    Neidhardt, H.3    Racec, P.N.4    Rehberg, J.5
  • 12
    • 4644287245 scopus 로고    scopus 로고
    • Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger- Maxwell equations
    • T. D'Aprile and D. Mugnai, Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004) 893-906. (Pubitemid 39604178)
    • (2004) Royal Society of Edinburgh - Proceedings A , vol.134 , Issue.5 , pp. 893-906
    • D'Aprile, T.1    Mugnai, D.2
  • 13
    • 4644368413 scopus 로고    scopus 로고
    • Non-existence results for the coupled Klein-Gordon-Maxwell equations
    • -, Non-existence results for the coupled Klein-Gordon-Maxwell equations, Adv. Nonlinear Stud. 4 (2004) 307-322. (Pubitemid 39289313)
    • (2004) Advanced Nonlinear Studies , vol.4 , Issue.3 , pp. 307-322
    • D'Aprile, T.1    Mugnai, D.2
  • 14
    • 30344442912 scopus 로고    scopus 로고
    • On bound states concentrating on spheres for the Maxwell-Schrödinger equation
    • T. D'Aprile and J. Wei, On bound states concentrating on spheres for the Maxwell-Schrödinger equation, SIAM J. Math. Anal. 37 (2005) 321-342.
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 321-342
    • D'aprile, T.1    Wei, J.2
  • 15
    • 30344459152 scopus 로고    scopus 로고
    • Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem
    • -, Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem, Calc. Var. Partial Differential Equations 25 (2005) 105-137.
    • (2005) Calc. Var. Partial Differential Equations , vol.25 , pp. 105-137
    • D'aprile, T.1    Wei, J.2
  • 16
    • 68249098342 scopus 로고    scopus 로고
    • Solutions of the Schrödinger-Poisson problem concentrating on spheres, part II: Existence
    • I. Ianni, Solutions of the Schrödinger-Poisson problem concentrating on spheres, part II: existence, Math. Models Methods Appl. Sci. 19(6) (2009) 1-37.
    • (2009) Math. Models Methods Appl. Sci. , vol.19 , Issue.6 , pp. 1-37
    • Ianni, I.1
  • 17
    • 49649091557 scopus 로고    scopus 로고
    • On concentration of positive bound states for the Schrödinger- Poisson problem with potentials
    • I. Ianni and G. Vaira, On concentration of positive bound states for the Schrödinger-Poisson problem with potentials, Adv. Nonlinear Stud. 8(3) (2008) 573-595.
    • (2008) Adv. Nonlinear Stud. , vol.8 , Issue.3 , pp. 573-595
    • Ianni, I.1    Vaira, G.2
  • 18
    • 67650035426 scopus 로고    scopus 로고
    • Solutions of the Schrödinger-Poisson problem concentrating on spheres, part I: Necessary conditions
    • -, Solutions of the Schrödinger-Poisson problem concentrating on spheres, part I: necessary conditions, Math. Models Methods Appl. Sci. 19(5) (2009) 1-14.
    • (2009) Math. Models Methods Appl. Sci. , vol.19 , Issue.5 , pp. 1-14
    • Ianni, I.1    Vaira, G.2
  • 22
    • 34247356227 scopus 로고    scopus 로고
    • On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations
    • DOI 10.1016/j.na.2006.07.029, PII S0362546X06004354
    • H. Kikuchi, On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations, Nonlinear Anal. 67(5) (2007) 1445-1456. (Pubitemid 46634814)
    • (2007) Nonlinear Analysis, Theory, Methods and Applications , vol.67 , Issue.5 , pp. 1445-1456
    • Kikuchi, H.1
  • 25
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations: The locally compact case, part 1
    • P.-L. Lions, The concentration-compactness principle in the calculus of variations: The locally compact case, part 1, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 109-145.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 109-145
    • Lions, P.-L.1
  • 26
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations: The locally compact case, part 2
    • -, The concentration-compactness principle in the calculus of variations: The locally compact case, part 2, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 223-283.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 223-283
    • Lions, P.-L.1
  • 27
    • 36849031785 scopus 로고    scopus 로고
    • Symmetry of minimizers for some nonlocal variational problems
    • O. Lopes and M. Maris, Symmetry of minimizers for some nonlocal variational problems, J. Funct. Anal. 254 (2008) 535-592.
    • (2008) J. Funct. Anal. , vol.254 , pp. 535-592
    • Lopes, O.1    Maris, M.2
  • 28
    • 0035427295 scopus 로고    scopus 로고
    • The Schrödinger-Poisson-Xα equation
    • N. J. Mauser, The Schrödinger-Poisson-Xα equation, Appl. Math. Lett. 14 (2001) 759-763.
    • (2001) Appl. Math. Lett. , vol.14 , pp. 759-763
    • Mauser, N.J.1
  • 29
  • 30
    • 39449135093 scopus 로고    scopus 로고
    • Neumann condition in the Schrödinger-Maxwell system
    • L. Pisani and G. Siciliano, Neumann condition in the Schrödinger- Maxwell system, Topol. Methods Nonlinear Anal. 29 (2007) 251-264.
    • (2007) Topol. Methods Nonlinear Anal. , vol.29 , pp. 251-264
    • Pisani, L.1    Siciliano, G.2
  • 31
    • 12144251987 scopus 로고    scopus 로고
    • Semiclassical states for coupled schrödinger-maxwell equations: Concentration around a sphere
    • DOI 10.1142/S0218202505003939
    • D. Ruiz, Semiclassical states for coupled Schrodinger-Maxwell equations: concentration around a sphere, Math. Models Methods Appl. Sci. 15 (2005) 141-164. (Pubitemid 40111656)
    • (2005) Mathematical Models and Methods in Applied Sciences , vol.15 , Issue.1 , pp. 141-164
    • Ruiz, D.1
  • 32
    • 33646917496 scopus 로고    scopus 로고
    • The Schrödinger-Poisson equation under the effect of a nonlinear local term
    • DOI 10.1016/j.jfa.2006.04.005, PII S0022123606001583
    • -, The Schrödinger-Poisson equation under the effect of a nonlinear local term, J. Funct. Anal. 237 (2006) 655-674. (Pubitemid 43792923)
    • (2006) Journal of Functional Analysis , vol.237 , Issue.2 , pp. 655-674
    • Ruiz, D.1
  • 33
    • 77956056995 scopus 로고    scopus 로고
    • On the Schrödinger-Poisson-Slater system: Behavior of minimizers, radial and nonradial cases
    • -, On the Schrödinger-Poisson-Slater system: Behavior of minimizers, radial and nonradial cases, Arch. Ration. Mech. Anal. 198 (2010) 349-368.
    • (2010) Arch. Ration. Mech. Anal. , vol.198 , pp. 349-368
    • Ruiz, D.1
  • 34
    • 3542992111 scopus 로고    scopus 로고
    • Long-time dynamics of the Schrödinger-Poisson-Slater system
    • O. Sánchez and J. Soler, Long-time dynamics of the Schrödinger-Poisson-Slater system, J. Statist. Phys. 114 (2004) 179-204.
    • (2004) J. Statist. Phys. , vol.114 , pp. 179-204
    • Sánchez, O.1    Soler, J.2
  • 35
    • 33846410438 scopus 로고
    • A simplification of the Hartree-Fock method
    • J. C. Slater, A simplification of the Hartree-Fock method, Phys. Rev. 81 (1951) 385-390.
    • (1951) Phys. Rev. , vol.81 , pp. 385-390
    • Slater, J.C.1
  • 36
    • 51249177065 scopus 로고
    • On the evolution of harmonic mappings of Riemannian surfaces
    • M. Struwe, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv. 60 (1985) 558-581.
    • (1985) Comment. Math. Helv. , vol.60 , pp. 558-581
    • Struwe, M.1
  • 37
    • 34547961548 scopus 로고    scopus 로고
    • Nonlinear Schrödinger equations with unbounded and decaying radial potentials
    • J. Su, Z.-Q. Wang and M. Willem, Nonlinear Schrödinger equations with unbounded and decaying radial potentials, Commun. Contemp. Math. 9 (2007) 571-583.
    • (2007) Commun. Contemp. Math. , vol.9 , pp. 571-583
    • Su, J.1    Wang, Z.-Q.2    Willem, M.3
  • 40
    • 65549153402 scopus 로고    scopus 로고
    • On the existence of solutions for the Schrödinger-Poisson equations
    • L. Zhao and F. Zhao, On the existence of solutions for the Schrödinger-Poisson equations, J. Math. Anal. Appl. 346 (2008) 155-169.
    • (2008) J. Math. Anal. Appl. , vol.346 , pp. 155-169
    • Zhao, L.1    Zhao, F.2


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