메뉴 건너뛰기




Volumn 40, Issue 1, 2008, Pages 365-381

Orbital stability of bound states of semiclassical nonlinear schrödinger equations with critical nonlinearity

Author keywords

Orbital stability; Spike; Trap potential

Indexed keywords

ASYMPTOTIC ANALYSIS; BOSE-EINSTEIN CONDENSATION; CONTROL NONLINEARITIES; NONLINEAR EQUATIONS; STEAM CONDENSERS;

EID: 54249127918     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/070683842     Document Type: Article
Times cited : (11)

References (37)
  • 1
    • 0031313734 scopus 로고    scopus 로고
    • Semiclassical states of nonlinear Schrödinger equations
    • A. AMBROSETTI, M. BADIALE, AND S. CINGOLANI, Semiclassical states of nonlinear Schrödinger equations, Arch. Ration. Mech. Anal., 140 (1997), pp. 285-300.
    • (1997) Arch. Ration. Mech. Anal , vol.140 , pp. 285-300
    • AMBROSETTI, A.1    BADIALE, M.2    CINGOLANI, S.3
  • 2
    • 33644966669 scopus 로고    scopus 로고
    • Bound and ground states of coupled nonlinear Schrödinger equations
    • A. AMBROSETTI AND E. COLORADO, Bound and ground states of coupled nonlinear Schrödinger equations, C. R. Math. Acad. Sci. Paris, 342 (2006), pp. 453-458.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.342 , pp. 453-458
    • AMBROSETTI, A.1    COLORADO, E.2
  • 3
    • 0038609648 scopus 로고    scopus 로고
    • Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part I
    • A. AMBROSETTI, A. MALCHIODI, AND W.-M. NI, Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part I, Comm. Math. Phys., 235 (2003), pp. 427-466.
    • (2003) Comm. Math. Phys , vol.235 , pp. 427-466
    • AMBROSETTI, A.1    MALCHIODI, A.2    NI, W.-M.3
  • 4
    • 38749138527 scopus 로고    scopus 로고
    • Bound states for a coupled Schrödinger system
    • T. BARTSCH, Z.-Q. WANG, AND J. WEI, Bound states for a coupled Schrödinger system, J. Fixed Point Theory Appl., 2 (2007), pp. 353-367.
    • (2007) J. Fixed Point Theory Appl , vol.2 , pp. 353-367
    • BARTSCH, T.1    WANG, Z.-Q.2    WEI, J.3
  • 5
    • 0000817006 scopus 로고
    • Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires
    • H. BERESTYCKI AND T. CAZENAVE, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sci. Paris Sér. I Math., 293 (1981), pp. 489-492.
    • (1981) C. R. Acad. Sci. Paris Sér. I Math , vol.293 , pp. 489-492
    • BERESTYCKI, H.1    CAZENAVE, T.2
  • 6
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • T. CAZENAVE AND P. L. LIONS, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85 (1982), pp. 549-561.
    • (1982) Comm. Math. Phys , vol.85 , pp. 549-561
    • CAZENAVE, T.1    LIONS, P.L.2
  • 8
    • 0031237479 scopus 로고    scopus 로고
    • Semiclassical states for nonlinear Schrödinger equation
    • M. DEL PINO AND P. FELMER, Semiclassical states for nonlinear Schrödinger equation, J. Funct. Anal., 149 (1997), pp. 245-265.
    • (1997) J. Funct. Anal , vol.149 , pp. 245-265
    • DEL PINO, M.1    FELMER, P.2
  • 9
    • 0036026058 scopus 로고    scopus 로고
    • Semiclassical states of nonlinear Schrödinger equations: A variational reduction method
    • M. DEL PINO AND P. FELMER, Semiclassical states of nonlinear Schrödinger equations: A variational reduction method, Math. Ann., 324 (2002), pp. 1-32.
    • (2002) Math. Ann , vol.324 , pp. 1-32
    • DEL PINO, M.1    FELMER, P.2
  • 11
    • 0001613187 scopus 로고
    • Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
    • A. FLOER AND A. WEINSTEIN, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal., 69 (1986), pp. 397-408.
    • (1986) J. Funct. Anal , vol.69 , pp. 397-408
    • FLOER, A.1    WEINSTEIN, A.2
  • 12
    • 27744441994 scopus 로고    scopus 로고
    • Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials
    • R. FUKUIZUMI, Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials, Adv. Differential Equations, 10 (2005), pp. 259-276.
    • (2005) Adv. Differential Equations , vol.10 , pp. 259-276
    • FUKUIZUMI, R.1
  • 13
    • 44449145089 scopus 로고    scopus 로고
    • Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential
    • to appear
    • R. FUKUIZUMI AND L. JEANJEAN, Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential, Discrete Contin. Dyn. Syst. to appear.
    • Discrete Contin. Dyn. Syst
    • FUKUIZUMI, R.1    JEANJEAN, L.2
  • 14
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry I
    • M. GRILLAKIS, J. SHATAH, AND W. STRAUSS, Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal., 74 (1987), pp. 160-197.
    • (1987) J. Funct. Anal , vol.74 , pp. 160-197
    • GRILLAKIS, M.1    SHATAH, J.2    STRAUSS, W.3
  • 15
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry II
    • M. GRILLAKIS, J. SHATAH, AND W. STRAUSS, Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal., 94 (1990), pp. 308-348.
    • (1990) J. Funct. Anal , vol.94 , pp. 308-348
    • GRILLAKIS, M.1    SHATAH, J.2    STRAUSS, W.3
  • 16
    • 0345135057 scopus 로고    scopus 로고
    • On the number of single-peaked solutions of the nonlinear Schrödinger equations
    • M. GROSSI, On the number of single-peaked solutions of the nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 19 (2002), pp. 261-280.
    • (2002) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.19 , pp. 261-280
    • GROSSI, M.1
  • 17
    • 0000616123 scopus 로고    scopus 로고
    • Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method
    • C. GUI, Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method, Comm. Partial Differential Equations, 21 (1996), pp. 787-820.
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 787-820
    • GUI, C.1
  • 19
    • 0000825718 scopus 로고    scopus 로고
    • On interacting bumps of semiclassical states of nonlinear Schrödinger equations
    • X. KANG AND J. WEI, On interacting bumps of semiclassical states of nonlinear Schrödinger equations, Adv. Differential Equations, 5 (2000), pp. 899-928.
    • (2000) Adv. Differential Equations , vol.5 , pp. 899-928
    • KANG, X.1    WEI, J.2
  • 21
    • 33747168470 scopus 로고    scopus 로고
    • Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials
    • T. C. LIN AND J. WEI, Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials, J. Differential Equations, 229 (2006), pp. 538-569.
    • (2006) J. Differential Equations , vol.229 , pp. 538-569
    • LIN, T.C.1    WEI, J.2
  • 22
    • 33846096848 scopus 로고    scopus 로고
    • Symbiotic bright solitary wave solutions of coupled nonlinear Schödinger equations
    • T. C. LIN AND J. WEI, Symbiotic bright solitary wave solutions of coupled nonlinear Schödinger equations, Nonlinearity, 19 (2006), pp. 2755-2773.
    • (2006) Nonlinearity , vol.19 , pp. 2755-2773
    • LIN, T.C.1    WEI, J.2
  • 23
    • 33747158213 scopus 로고    scopus 로고
    • Positive solutions for a weakly coupled non-linear Schrödinger system
    • L. A. MAIA, E. MONTEFUSCO, AND B. PELLACCI, Positive solutions for a weakly coupled non-linear Schrödinger system, J. Differential Equations, 229 (2006), pp. 743-767.
    • (2006) J. Differential Equations , vol.229 , pp. 743-767
    • MAIA, L.A.1    MONTEFUSCO, E.2    PELLACCI, B.3
  • 24
    • 33244481059 scopus 로고    scopus 로고
    • D. MIHALACHE, D. MAZILU, F. LEDERER, B. A. MALOMED, L.-C. CRASOVAN, Y. V. KARTASHOV, AND L. TORNER, Stable three-dimensional solitons in attractive Bose-Einstein condensates loaded in an optical lattice, Phys. Rev. A, 72 (2005), article 021601.
    • D. MIHALACHE, D. MAZILU, F. LEDERER, B. A. MALOMED, L.-C. CRASOVAN, Y. V. KARTASHOV, AND L. TORNER, Stable three-dimensional solitons in attractive Bose-Einstein condensates loaded in an optical lattice, Phys. Rev. A, 72 (2005), article 021601.
  • 25
    • 0000998584 scopus 로고
    • On positive multi-bump states of nonlinear Schrödinger equation under multiple well potentials
    • Y.-G. OH, On positive multi-bump states of nonlinear Schrödinger equation under multiple well potentials, Comm. Math. Phys., 131 (1990), pp. 223-253.
    • (1990) Comm. Math. Phys , vol.131 , pp. 223-253
    • OH, Y.-G.1
  • 26
    • 0002776502 scopus 로고
    • Stability of semiclassical bound state of nonlinear Schrödinger equations with potentials
    • Y.-G. OH, Stability of semiclassical bound state of nonlinear Schrödinger equations with potentials, Comm. Math. Phys., 121 (1989), pp. 11-33.
    • (1989) Comm. Math. Phys , vol.121 , pp. 11-33
    • OH, Y.-G.1
  • 29
    • 34249835055 scopus 로고
    • On a class of nonlinear Schrödinger equations
    • P. RABINOWITZ, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys., 43 (1992), pp. 270-291.
    • (1992) Z. Angew. Math. Phys , vol.43 , pp. 270-291
    • RABINOWITZ, P.1
  • 31
    • 33847197945 scopus 로고    scopus 로고
    • Least energy solitary waves for a system of nonlinear Schrödinger equations
    • to appear
    • B. SIRAKOV, Least energy solitary waves for a system of nonlinear Schrödinger equations, Comm. Math. Phys., to appear.
    • Comm. Math. Phys
    • SIRAKOV, B.1
  • 32
    • 34250081368 scopus 로고
    • On concentration of positive bound states of nonlinear Schrödinger equations
    • X. WANG, On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys., 153 (1993), pp. 229-243.
    • (1993) Comm. Math. Phys , vol.153 , pp. 229-243
    • WANG, X.1
  • 33
    • 0033589578 scopus 로고    scopus 로고
    • Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
    • Z.-Q. WANG, Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations, 159 (1999), pp. 102-137.
    • (1999) J. Differential Equations , vol.159 , pp. 102-137
    • WANG, Z.-Q.1
  • 34
    • 0030578649 scopus 로고    scopus 로고
    • On the construction of single-peaked solutions to a singularly perturbed elliptic Dirichlet problem
    • J. WEI, On the construction of single-peaked solutions to a singularly perturbed elliptic Dirichlet problem, J. Differential Equations, 129 (1996), pp. 315-333.
    • (1996) J. Differential Equations , vol.129 , pp. 315-333
    • WEI, J.1
  • 35
    • 0347188202 scopus 로고    scopus 로고
    • On the interior spike layer solutions for some singular perturbation problems
    • J. WEI, On the interior spike layer solutions for some singular perturbation problems, Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), pp. 849-874.
    • (1998) Proc. Roy. Soc. Edinburgh Sect. A , vol.128 , pp. 849-874
    • WEI, J.1
  • 36
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M. WEINSTEIN, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys., 87 (1983), pp. 567-576.
    • (1983) Comm. Math. Phys , vol.87 , pp. 567-576
    • WEINSTEIN, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.