메뉴 건너뛰기




Volumn 9, Issue 4, 2007, Pages 571-583

Nonlinear schrödinger equations with unbounded and decaying radial potentials

Author keywords

Ground states; Nonlinear schr dinger equations; Unbounded or decaying potentials

Indexed keywords


EID: 34547961548     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021919970700254X     Document Type: Article
Times cited : (131)

References (32)
  • 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. 7 (2005) 117-144.
    • (2005) J. Eur. Math. Soc , vol.7 , pp. 117-144
    • Ambrosetti, A.1    Felli, V.2    Malchiodi, A.3
  • 2
    • 0038609648 scopus 로고    scopus 로고
    • Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres. I
    • A. Ambrosetti, A. Malchiodi and W.-M. Ni, Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres. I, Comm. Math. Phys. 235 (2003) 427-466.
    • (2003) Comm. Math. Phys , vol.235 , pp. 427-466
    • Ambrosetti, A.1    Malchiodi, A.2    Ni, W.-M.3
  • 3
    • 33748570781 scopus 로고    scopus 로고
    • Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity
    • A. Ambrosetti, A. Malchiodi and D. Ruiz, Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. Anal. Math. 98 (2006) 317-348.
    • (2006) J. Anal. Math , vol.98 , pp. 317-348
    • Ambrosetti, A.1    Malchiodi, A.2    Ruiz, D.3
  • 4
    • 33751058685 scopus 로고    scopus 로고
    • Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials
    • A. Ambrosetti and D. Ruiz, Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials, Proc. Roy. Soc. Edinburgh Sect. A 136(5) (2006) 889-907.
    • (2006) Proc. Roy. Soc. Edinburgh Sect. A , vol.136 , Issue.5 , pp. 889-907
    • Ambrosetti, A.1    Ruiz, D.2
  • 5
    • 33745663525 scopus 로고    scopus 로고
    • Nonlinear Schrödinger equations with vanishing and decaying potentials
    • A. Ambrosetti and Z.-Q. Wang, Nonlinear Schrödinger equations with vanishing and decaying potentials, Differ. Integral. Equations 18 (2005) 1321-1332.
    • (2005) Differ. Integral. Equations , vol.18 , pp. 1321-1332
    • Ambrosetti, A.1    Wang, Z.-Q.2
  • 6
    • 84887491883 scopus 로고    scopus 로고
    • A note on nonlinear elliptic problems with singular potentials
    • M. Badiale and S. Rolando, A note on nonlinear elliptic problems with singular potentials, Rend. Lincei Mat. Appl. 17 (2006) 1-13.
    • (2006) Rend. Lincei Mat. Appl , vol.17 , pp. 1-13
    • Badiale, M.1    Rolando, S.2
  • 8
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations. I. Existence of a ground state
    • H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Ration. Mech. Anal. 82 (1983) 313-345.
    • (1983) Arch. Ration. Mech. Anal , vol.82 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 9
    • 0036027321 scopus 로고    scopus 로고
    • Standing waves with a critical frequency for nonlinear Schrödinger equations
    • J. Byeon and Z.-Q. Wang, Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal. 165 (2002) 295-316.
    • (2002) Arch. Ration. Mech. Anal , vol.165 , pp. 295-316
    • Byeon, J.1    Wang, Z.-Q.2
  • 10
    • 0142230503 scopus 로고    scopus 로고
    • Standing waves with a critical frequency for nonlinear Schrödinger equations, II
    • J. Byeon and Z.-Q. Wang, Standing waves with a critical frequency for nonlinear Schrödinger equations, II, Calc. Var. Partial Differential Equations 18 (2003) 207-219.
    • (2003) Calc. Var. Partial Differential Equations , vol.18 , pp. 207-219
    • Byeon, J.1    Wang, Z.-Q.2
  • 11
    • 33745655598 scopus 로고    scopus 로고
    • Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potential
    • J. Byeon and Z.-Q. Wang, Spherical semiclassical states of a critical frequency for Schrödinger equations with decaying potential, J. Eur. Math. Soc. 8 (2006) 217-228.
    • (2006) J. Eur. Math. Soc , vol.8 , pp. 217-228
    • Byeon, J.1    Wang, Z.-Q.2
  • 12
    • 0039030643 scopus 로고    scopus 로고
    • On the existence of positive solutions for a class of singular elliptic equations
    • M. Conti, S. Crotti and D. Pardo, On the existence of positive solutions for a class of singular elliptic equations, Adv. Differential Equations 3 (1998) 111-132.
    • (1998) Adv. Differential Equations , vol.3 , pp. 111-132
    • Conti, M.1    Crotti, S.2    Pardo, D.3
  • 13
    • 33644814735 scopus 로고    scopus 로고
    • Nodal solutions to a class of nonstandard superlinear equations on M
    • M. Conti, S. Terracini and G. Verzini, Nodal solutions to a class of nonstandard superlinear equations on M, Adv. Differential Equations 7 (2002) 297-318.
    • (2002) Adv. Differential Equations , vol.7 , pp. 297-318
    • Conti, M.1    Terracini, S.2    Verzini, G.3
  • 15
    • 34250124360 scopus 로고
    • On the existence of positive entire solutions of a semilinear elliptic equation
    • W. Ding and W.-M. Ni, On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Ration. Mech. Anal. 91 (1986) 283-308.
    • (1986) Arch. Ration. Mech. Anal , vol.91 , pp. 283-308
    • Ding, W.1    Ni, W.-M.2
  • 16
    • 0010299677 scopus 로고
    • A family of optimal conditions for the absence of bound states in a potential
    • eds. E. H. Lieb, B. Simon and A. S. Wightman Princeton University Press
    • V. Glaser, A. Martin, H. Grosse and W. Thirring, A family of optimal conditions for the absence of bound states in a potential, in Studies in Mathematical Physics, eds. E. H. Lieb, B. Simon and A. S. Wightman (Princeton University Press, 1976), pp. 169-194.
    • (1976) Studies in Mathematical Physics , pp. 169-194
    • Glaser, V.1    Martin, A.2    Grosse, H.3    Thirring, W.4
  • 17
    • 0000956029 scopus 로고
    • Nonautonomous nonlinear scalar field equations
    • Y. Y. Li, Nonautonomous nonlinear scalar field equations, Indiana Univ. Math. J. 39 (1990) 283-301.
    • (1990) Indiana Univ. Math. J , vol.39 , pp. 283-301
    • Li, Y.Y.1
  • 19
    • 0000298073 scopus 로고
    • Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
    • E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. 118 (1983) 349-374.
    • (1983) Ann. of Math , vol.118 , pp. 349-374
    • Lieb, E.1
  • 21
    • 0001755361 scopus 로고
    • A nonlinear Dirichlet problem on the unit ball and its applications
    • W.-M. Ni, A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J. 31 (1982) 801-807.
    • (1982) Indiana Univ. Math. J , vol.31 , pp. 801-807
    • Ni, W.-M.1
  • 23
    • 0000520530 scopus 로고
    • Homoclinic orbits for a class of Hamiltonian systems
    • W. Omana and M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Differ. Integral Equations 5(5) (1992) 1115-1120.
    • (1992) Differ. Integral Equations , vol.5 , Issue.5 , pp. 1115-1120
    • Omana, W.1    Willem, M.2
  • 24
    • 0003997917 scopus 로고
    • Hardy-Type Inequalities, Pitman Res
    • Longman Scientific & Technical, Harlow
    • B. Opic and A. Kufner, Hardy-Type Inequalities, Pitman Res. Notes in Math. Series, Vol. 219 (Longman Scientific & Technical, Harlow, 1990).
    • (1990) Series. Notes in Math , vol.219
    • Opic, B.1    Kufner, A.2
  • 25
    • 34249835055 scopus 로고
    • On a class of nonlinear Schrödinger equations
    • P. H. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43(2) (1992) 270-291.
    • (1992) Z. Angew. Math. Phys , vol.43 , Issue.2 , pp. 270-291
    • Rabinowitz, P.H.1
  • 27
    • 34547955759 scopus 로고    scopus 로고
    • N with unbounded coefficients, in Variational and Topological Methods in the Study of Nonlinear Phenomena (Pisa, 2000), Progr. Nonlinear Differential Equations Appl., 49 (Birkhäuser Boston, Boston, MA, 2002), pp. 105-113.
    • N with unbounded coefficients, in Variational and Topological Methods in the Study of Nonlinear Phenomena (Pisa, 2000), Progr. Nonlinear Differential Equations Appl., Vol. 49 (Birkhäuser Boston, Boston, MA, 2002), pp. 105-113.
  • 30
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher dimensions
    • W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55(2) (1977) 149-162.
    • (1977) Comm. Math. Phys , vol.55 , Issue.2 , pp. 149-162
    • Strauss, W.A.1
  • 31
    • 0000155087 scopus 로고    scopus 로고
    • On positive entire solutions to a class of equations with a singular coefficient and critical exponent
    • S. Terracini, On positive entire solutions to a class of equations with a singular coefficient and critical exponent, Adv. Differential Equations 1 (1996) 241-264.
    • (1996) Adv. Differential Equations , vol.1 , pp. 241-264
    • Terracini, S.1
  • 32
    • 0141726753 scopus 로고    scopus 로고
    • Caffarelli-Kohn-Nirenberg inequalities with remainder terms
    • Z.-Q. Wang and M. Willem, Caffarelli-Kohn-Nirenberg inequalities with remainder terms, J. Funct. Anal. 203 (2003) 550-568.
    • (2003) J. Funct. Anal , vol.203 , pp. 550-568
    • Wang, Z.-Q.1    Willem, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.