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Volumn 25, Issue 1, 2006, Pages 105-137

Standing waves in the Maxwell-Schrödinger equation and an optimal configuration problem

Author keywords

Localized energy method; Maxwell Schr dinger equations; Optimal configuration

Indexed keywords


EID: 30344459152     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-005-0342-9     Document Type: Article
Times cited : (70)

References (43)
  • 1
    • 0031313734 scopus 로고    scopus 로고
    • Semiclassical states of nonlinear Schrödinger equations
    • Ambrosetti, A., Badiale, M., Cingolani, S.: Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal. 140, 285-300 (1997)
    • (1997) Arch. Rat. Mech. Anal. , vol.140 , pp. 285-300
    • Ambrosetti, A.1    Badiale, M.2    Cingolani, S.3
  • 2
    • 0040435197 scopus 로고    scopus 로고
    • Multiplicity results for some nonlinear Schrödinger equations with potentials
    • Ambrosetti, A., Malchiodi, A., Secchi, S.: Multiplicity results for some nonlinear Schrödinger equations with potentials, Arch. Ration. Mech. Anal. 159(3), 253-271 (2001)
    • (2001) Arch. Ration. Mech. Anal. , vol.159 , Issue.3 , pp. 253-271
    • Ambrosetti, A.1    Malchiodi, A.2    Secchi, S.3
  • 3
    • 0001036379 scopus 로고    scopus 로고
    • An eigenvalue problem for the Schrödinger-Maxwell equations
    • Benci, V., Fortunato, D.: An eigenvalue problem for the Schrödinger-Maxwell equations, Top. Meth. Nonlinear Anal. 11(2), 283-293 (1998)
    • (1998) Top. Meth. Nonlinear Anal. , vol.11 , Issue.2 , pp. 283-293
    • Benci, V.1    Fortunato, D.2
  • 4
    • 23044530537 scopus 로고    scopus 로고
    • The Gierer & Meinhardt system: The breaking of homopclinics and multi-bump ground states
    • Chen, X., Del Pino, M., Kowalczyk, M.: The Gierer & Meinhardt system: the breaking of homopclinics and multi-bump ground states, Comm. Contemp. Math. 3, 419-439 (2001)
    • (2001) Comm. Contemp. Math. , vol.3 , pp. 419-439
    • Chen, X.1    Del Pino, M.2    Kowalczyk, M.3
  • 7
    • 0034165051 scopus 로고    scopus 로고
    • A note on asymptotic uniqueness for some nonlinearities which change sign
    • Dancer, E.N.: A note on asymptotic uniqueness for some nonlinearities which change sign, Bull. Austral. Math. Soc. 61, 305-312 (2000)
    • (2000) Bull. Austral. Math. Soc. , vol.61 , pp. 305-312
    • Dancer, E.N.1
  • 8
    • 0000650326 scopus 로고    scopus 로고
    • Multipeak solutions for a sing ular perturbed Neumann problem
    • Dancer, E.N., Yan, S.: Multipeak solutions for a sing ular perturbed Neumann problem, Pacific J. Math. 189, 241-262 (1999)
    • (1999) Pacific J. Math. , vol.189 , pp. 241-262
    • Dancer, E.N.1    Yan, S.2
  • 9
    • 4644244622 scopus 로고    scopus 로고
    • Semiclassical states for the nonlinear Schrödinger equation with the electromagnetic field
    • to appear
    • D'Aprile, T.: Semiclassical states for the nonlinear Schrödinger equation with the electromagnetic field, NoDEA Nonlinear Differential Equations Appl., to appear.
    • NoDEA Nonlinear Differential Equations Appl.
    • D'Aprile, T.1
  • 10
    • 4644287245 scopus 로고    scopus 로고
    • Existence of solitary waves for the nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations
    • D'Aprile, T., Mugnai, D.: Existence of solitary waves for the nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations, Proc. Roy. Soc. Edinburgh Sect. A 134(5), 893-906
    • Proc. Roy. Soc. Edinburgh Sect. A , vol.134 , Issue.5 , pp. 893-906
    • D'Aprile, T.1    Mugnai, D.2
  • 11
    • 30344442912 scopus 로고    scopus 로고
    • On Bound states concentrating on spheres for the Maxwell-Schrödinger equation
    • D'Aprile, T., Wei, J.: On Bound states concentrating on spheres for the Maxwell-Schrödinger equation, SIAM J. Math. Anal. 37(1), 321-342 (2005)
    • (2005) SIAM J. Math. Anal. , vol.37 , Issue.1 , pp. 321-342
    • D'Aprile, T.1    Wei, J.2
  • 12
    • 0001341199 scopus 로고    scopus 로고
    • Local mountain passes for semilinear elliptic problems in un-bounded domains
    • Del Pino, M., Felmer, P.: Local mountain passes for semilinear elliptic problems in un-bounded domains, Calc. Var. PDE 4(2), 121-137 (1996)
    • (1996) Calc. Var. PDE , vol.4 , Issue.2 , pp. 121-137
    • Del Pino, M.1    Felmer, P.2
  • 13
    • 0000260189 scopus 로고    scopus 로고
    • Multi-peak bound states for nonlinear Schr̈dinger equations
    • Del Pino, M., Felmer, P.: Multi-peak bound states for nonlinear Schr̈dinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 15(2), 127-149 (1998)
    • (1998) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.15 , Issue.2 , pp. 127-149
    • Del Pino, M.1    Felmer, P.2
  • 14
    • 0031237479 scopus 로고    scopus 로고
    • Semi-classical states for nonlinear Schrödinger equations
    • Del Pino, M., Felmer, P.: Semi-classical states for nonlinear Schrödinger equations, J. Funct. Anal. 149(1), 245-265 (1997)
    • (1997) J. Funct. Anal. , vol.149 , Issue.1 , pp. 245-265
    • Del Pino, M.1    Felmer, P.2
  • 15
    • 0036026058 scopus 로고    scopus 로고
    • Semi-classical states of nonlinear Schrödinger equations: A variational reduction method
    • Del Pino, M., 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, M.1    Felmer, P.2
  • 16
    • 0033233496 scopus 로고    scopus 로고
    • On the role of mean curvature in some singularly perturbed Neumann problems
    • Del Pino, M., Felmer, P., Wei, J.: On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal. 31(1), 63-79 (1999)
    • (1999) SIAM J. Math. Anal. , vol.31 , Issue.1 , pp. 63-79
    • Del Pino, M.1    Felmer, P.2    Wei, J.3
  • 18
    • 0003448545 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, Rhode Island
    • Evans, L.C.: Partial Differential Equations, American Mathematical Society, Providence, Rhode Island (1998).
    • (1998) Partial Differential Equations
    • Evans, L.C.1
  • 19
    • 0001613187 scopus 로고
    • Nonspreading wave pockets for the cubic Schrödinger equation with a bounded potential
    • Floer, A., Weinstein, A.: Nonspreading wave pockets 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
  • 22
    • 0034356993 scopus 로고    scopus 로고
    • Some results on a class of nonlinear Schrödinger equations
    • Grossi, M.: Some results on a class of nonlinear Schrödinger equations, Math. Z. 235(4), 687-705 (2000)
    • (2000) Math. Z. , vol.235 , Issue.4 , pp. 687-705
    • Grossi, M.1
  • 23
    • 0003226251 scopus 로고    scopus 로고
    • Existence of mullipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory
    • Grossi, M., Pistoia, A., Wei, J.: Existence of mullipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Calc. Var. PDE 11(2), 143-175 (2000)
    • (2000) Calc. Var. PDE , vol.11 , Issue.2 , pp. 143-175
    • Grossi, M.1    Pistoia, A.2    Wei, J.3
  • 24
    • 0000860177 scopus 로고    scopus 로고
    • Multipeak solutions for a semilinear Neumann problem
    • Gui, C.: Multipeak solutions for a semilinear Neumann problem, Duke Math. J. 84(3), 739-769 (1996)
    • (1996) Duke Math. J. , vol.84 , Issue.3 , pp. 739-769
    • Gui, C.1
  • 25
    • 0002610597 scopus 로고    scopus 로고
    • Multiple interior peak solutions for some singularly perturbed Neumann problems
    • Gui, C., Wei, J.: Multiple interior peak solutions for some singularly perturbed Neumann problems, J. Differ. Equations 158(1), 1-27 (1999)
    • (1999) J. Differ. Equations , vol.158 , Issue.1 , pp. 1-27
    • Gui, C.1    Wei, J.2
  • 26
    • 0034380572 scopus 로고    scopus 로고
    • On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems
    • Gui, C., Wei, J.: On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad. J. Math. 52(3), 522-538 (2000)
    • (2000) Canad. J. Math. , vol.52 , Issue.3 , pp. 522-538
    • Gui, C.1    Wei, J.2
  • 27
    • 0002025752 scopus 로고    scopus 로고
    • Multiple boundary peak solutions for some singularly perturbed Neumann problems
    • Gui, C., Wei, J., Winter, M.: Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17(1), 47-82 (2000)
    • (2000) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.17 , Issue.1 , pp. 47-82
    • Gui, C.1    Wei, J.2    Winter, M.3
  • 28
    • 0000825718 scopus 로고    scopus 로고
    • On interacting bumps of semiclassical states of nonlinear Schrödinger equations
    • Kang, X., Wei, J.: On interacting bumps of semiclassical states of nonlinear Schrödinger equations, Adv. Diff. Eqns. 5, 899-928 (2000)
    • (2000) Adv. Diff. Eqns. , vol.5 , pp. 899-928
    • Kang, X.1    Wei, J.2
  • 30
    • 0000264842 scopus 로고    scopus 로고
    • On a singularly perturbed elliptic equation
    • Li, Y.Y.: On a singularly perturbed elliptic equation, Adv. Differ. Equ. 6(2), 955-980 (1997)
    • (1997) Adv. Differ. Equ. , vol.6 , Issue.2 , pp. 955-980
    • Li, Y.Y.1
  • 31
    • 0000984635 scopus 로고    scopus 로고
    • On a singularly perturbed equation with Neumann boundary conditions
    • Li, Y.Y.: On a singularly perturbed equation with Neumann boundary conditions, Commun. PDE 23(3-4), 487-545 (1998)
    • (1998) Commun. PDE , vol.23 , Issue.3-4 , pp. 487-545
    • Li, Y.Y.1
  • 32
    • 84990581933 scopus 로고
    • Locating the peaks of least-energy solutions to a semilinear Neumann problem
    • Ni, W.M., Takagi, I.: Locating the peaks of least-energy solutions to a semilinear Neumann problem, Comm. Pure App. Math. 41(7), 819-851 (1991)
    • (1991) Comm. Pure App. Math. , vol.41 , Issue.7 , pp. 819-851
    • Ni, W.M.1    Takagi, I.2
  • 33
    • 84971179248 scopus 로고
    • On the shape of least-energy solutions to a semi-linear Neumann problem
    • Ni, W.M., Takagi, I.: On the shape of least-energy solutions to a semi-linear Neumann problem, Duke Math. J. 70, 247-281 (1993)
    • (1993) Duke Math. J. , vol.70 , pp. 247-281
    • Ni, W.M.1    Takagi, I.2
  • 35
    • 84990662413 scopus 로고
    • On the location and profile of spike-layer solutions to singularly perturbed semilinaer Dirichlet problems
    • Ni, W.M., Wei, J.: On the location and profile of spike-layer solutions to singularly perturbed semilinaer Dirichlet problems, Comm. Pure. Appl. Math. 48, 731-768 (1995)
    • (1995) Comm. Pure. Appl. Math. , vol.48 , pp. 731-768
    • Ni, W.M.1    Wei, J.2
  • 36
    • 0000483708 scopus 로고    scopus 로고
    • On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems: Intermediate solutions
    • Ni, W.M., Takagi, I., Wei, J.: On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems: intermediate solutions, Duke Math. J. 94, 597-618 (1998)
    • (1998) Duke Math. J. , vol.94 , pp. 597-618
    • Ni, W.M.1    Takagi, I.2    Wei, J.3
  • 38
    • 0000998584 scopus 로고
    • On positive multi-lump bound states of nonlinear Schrödinger equation under multiple well potential
    • Oh, Y.J.: On positive multi-lump bound states of nonlinear Schrödinger equation under multiple well potential, Comm. Math. Phys. 131, 223-253 (1990)
    • (1990) Comm. Math. Phys. , vol.131 , pp. 223-253
    • Oh, Y.J.1
  • 39
    • 34249835055 scopus 로고
    • On a class of nonlinear Schrödinger equations
    • Rabinowitz, P.: On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43, 270-291 (1992)
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 270-291
    • Rabinowitz, P.1
  • 40
    • 34250081368 scopus 로고
    • On concentration of positive bound states of nonlinear Schrödinger equations
    • Wang, X.: On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153(2), 229-244 (1993)
    • (1993) Comm. Math. Phys. , vol.153 , Issue.2 , pp. 229-244
    • Wang, X.1
  • 41
    • 0031562011 scopus 로고    scopus 로고
    • On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem
    • Wei, J.: On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem, J. Differ. Equations, 134, 104-133 (1997)
    • (1997) J. Differ. Equations , vol.134 , pp. 104-133
    • Wei, J.1
  • 42
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem
    • Wei, J.: On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differ. Equations 129(2), 315-333 (1996)
    • (1996) J. Differ. Equations , vol.129 , Issue.2 , pp. 315-333
    • Wei, J.1
  • 43
    • 18144380867 scopus 로고    scopus 로고
    • Symmetric and asymmetric multiple clusters in a reaction-diffusion system
    • to appear
    • Wei, J., Winter, M.: Symmetric and asymmetric multiple clusters in a reaction-diffusion system, NoDEA Nonlinear Differential Equations Appl., to appear.
    • NoDEA Nonlinear Differential Equations Appl.
    • Wei, J.1    Winter, M.2


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