메뉴 건너뛰기




Volumn 189, Issue 2, 2010, Pages 273-301

Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity

Author keywords

Decay of solutions; Degenerate potentials; Moser iteration scheme; Regularity theory; Stationary nonlinear Schr dinger equation; Trace inequalities; Weighted Sobolev spaces

Indexed keywords


EID: 77949423891     PISSN: 03733114     EISSN: 16181891     Source Type: Journal    
DOI: 10.1007/s10231-009-0109-6     Document Type: Article
Times cited : (65)

References (21)
  • 1
    • 0003034107 scopus 로고
    • A trace inequality for generalized potentials
    • Adams D.: A trace inequality for generalized potentials. Stud. Math. 48, 99-105 (1973).
    • (1973) Stud. Math. , vol.48 , pp. 99-105
    • Adams, D.1
  • 2
    • 12844261727 scopus 로고    scopus 로고
    • Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
    • Ambrosetti A., Felli V., Malchiodi A.: Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Eur. Math. Soc. 7(1), 117-144 (2005).
    • (2005) J. Eur. Math. Soc. , 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
    • Ambrosetti A., Malchiodi A., Ruiz D.: Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Anal. Math. 98, 317-348 (2006).
    • (2006) J. Anal. Math. , vol.98 , pp. 317-348
    • Ambrosetti, A.1    Malchiodi, A.2    Ruiz, D.3
  • 4
    • 0033114779 scopus 로고    scopus 로고
    • On the best Sobolev inequality
    • Aubin T., Li Y. Y.: On the best Sobolev inequality. J. Math. Pures Appl. 78(4), 353-387 (1999).
    • (1999) J. Math. Pures Appl. , vol.78 , Issue.4 , pp. 353-387
    • Aubin, T.1    Li, Y.Y.2
  • 5
    • 48249101992 scopus 로고    scopus 로고
    • Bound state solutions for a class of nonlinear Schrödinger equations
    • Bonheure D., van Schaftinegn J.: Bound state solutions for a class of nonlinear Schrödinger equations. Rev. Mat. Iberoamericana 24, 297-351 (2008).
    • (2008) Rev. Mat. Iberoamericana , vol.24 , pp. 297-351
    • Bonheure, D.1    van Schaftinegn, J.2
  • 6
    • 0001735158 scopus 로고
    • Remarks on the Schrödinger operator with singular complex potentials
    • Brezis H., Kato T. L.: Remarks on the Schrödinger operator with singular complex potentials. J. Math. Pures Appl. 58(2), 137-151 (1979).
    • (1979) J. Math. Pures Appl. , vol.58 , Issue.2 , pp. 137-151
    • Brezis, H.1    Kato, T.L.2
  • 7
    • 0001341199 scopus 로고    scopus 로고
    • Local mountain passes for semilinear elliptic problems in unbounded domains
    • del Pino M., Felmer P.: Local mountain passes for semilinear elliptic problems in unbounded domains. Calc. Var. Partial Differ. Equ. 4, 121-137 (1996).
    • (1996) Calc. Var. Partial Differ. Equ. , vol.4 , pp. 121-137
    • del Pino, M.1    Felmer, P.2
  • 8
    • 0036026058 scopus 로고    scopus 로고
    • Semi-classical states of nonlinear Schrödinger equations: A variational reduction method
    • del Pino N., Felmer P.: Semi-classical states of nonlinear Schrödinger equations: a variational reduction method. Math. Ann. 324(1), 1-32 (2002).
    • (2002) Math. Ann. , vol.324 , Issue.1 , pp. 1-32
    • del Pino, N.1    Felmer, P.2
  • 9
    • 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(3), 397-408 (1986).
    • (1986) J. Funct. Anal. , vol.69 , Issue.3 , pp. 397-408
    • Floer, A.1    Weinstein, A.2
  • 10
    • 0003265439 scopus 로고
    • Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
    • Cambridge: Cambridge University Press
    • Mattila P.: Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability. Cambridge Studies in Advanced Mathematics, vol. 44. Cambridge University Press, Cambridge (1995).
    • (1995) Cambridge Studies in Advanced Mathematics , vol.44
    • Mattila, P.1
  • 11
    • 0003796632 scopus 로고
    • Sobolev Spaces
    • Springer, Berlin, Translated from the Russian by Shaposhnikova, T.O
    • Maz'ja, V. G.: Sobolev Spaces. Springer Series in Soviet Mathematics, Springer, Berlin, Translated from the Russian by Shaposhnikova, T. O. (1985).
    • (1985) Springer Series in Soviet Mathematics
    • Maz'ja, V.G.1
  • 12
    • 0003002827 scopus 로고    scopus 로고
    • Diffusion, cross-diffusion, and their spike-layer steady states
    • Ni W.-M.: Diffusion, cross-diffusion, and their spike-layer steady states. Notices Am. Math. Soc. 45(1), 9-18 (1998).
    • (1998) Notices Am. Math. Soc. , vol.45 , Issue.1 , pp. 9-18
    • Ni, W.-M.1
  • 13
    • 0000973918 scopus 로고
    • On elliptic partial differential equations
    • Nirenberg L.: On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa 13(3), 115-162 (1959).
    • (1959) Ann. Scuola Norm. Sup. Pisa , vol.13 , Issue.3 , pp. 115-162
    • Nirenberg, L.1
  • 15
    • 0001469934 scopus 로고
    • Espaces d'interpolation et théorème de Soboleff
    • Peetre J.: Espaces d'interpolation et théorème de Soboleff. Annales de l'institut Fourier 16(1), 279-317 (1966).
    • (1966) Annales De L'institut Fourier , vol.16 , Issue.1 , pp. 279-317
    • Peetre, J.1
  • 16
    • 34249835055 scopus 로고
    • On a class of nonlinear Schrödinger equations
    • Rabinowitz P. H.: On a class of nonlinear Schrödinger equations. Z. Angew. Math. Phys. 43(2), 270-291 (1992).
    • (1992) Z. Angew. Math. Phys. , vol.43 , Issue.2 , pp. 270-291
    • Rabinowitz, P.H.1
  • 17
    • 0036778761 scopus 로고    scopus 로고
    • Compact embeddings and indefinite semilinear elliptic problems
    • Schneider M.: Compact embeddings and indefinite semilinear elliptic problems. Nonlinear Anal. Ser A Theory Methods 51(2), 283-303 (2002).
    • (2002) Nonlinear Anal. Ser A Theory Methods , vol.51 , Issue.2 , pp. 283-303
    • Schneider, M.1
  • 19
    • 0000471156 scopus 로고
    • Remarks concerning the conformal deformation of Riemannian structures on compact manifolds
    • Trudinger N. S.: Remarks concerning the conformal deformation of Riemannian structures on compact manifolds. Ann. Scuola Norm. Sup. Pisa 22(3), 265-274 (1968).
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , Issue.3 , pp. 265-274
    • Trudinger, N.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.