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Volumn 9, Issue 3, 2010, Pages 741-750

A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities

Author keywords

Ground state solutions; Nehari manifold; Nonlinear Schr dinger systems

Indexed keywords


EID: 77249105607     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2010.9.741     Document Type: Article
Times cited : (14)

References (30)
  • 1
    • 0001237446 scopus 로고    scopus 로고
    • Partially coherent solitons on a finite background
    • N. Akhmediev and A. Ankiewicz, Partially coherent solitons on a finite background, Phys. Rev. Lett., 82 (1999), 2661-2664.
    • (1999) Phys. Rev. Lett , vol.82 , pp. 2661-2664
    • Akhmediev, N.1    Ankiewicz, A.2
  • 2
    • 36348990860 scopus 로고    scopus 로고
    • Standing waves of some coupled nonlinear Schrödinger equations
    • A. Ambrosetti and E. Colorado, Standing waves of some coupled nonlinear Schrödinger equations, J. Lond. Math. Soc., 75 (2007), 67-82.
    • (2007) J. Lond. Math. Soc , vol.75 , pp. 67-82
    • Ambrosetti, A.1    Colorado, E.2
  • 3
    • 33846060400 scopus 로고    scopus 로고
    • Existence of solutions for elliptic systems with critical Sobolev exponent
    • electronic, 13 pp
    • P. Amster, P. De Nápoli and M. C. Mariani, Existence of solutions for elliptic systems with critical Sobolev exponent, Electron. J. Differential Equations, 49 (2002), 13 pp. (electronic).
    • (2002) Electron. J. Differential Equations , vol.49
    • Amster, P.1    De Nápoli, P.2    Mariani, M.C.3
  • 4
    • 69549110672 scopus 로고    scopus 로고
    • N under the effect of a general nonlinear term, Indiana Univ. Journal 58 (2009), 1361-1378.
    • N under the effect of a general nonlinear term, Indiana Univ. Journal 58 (2009), 1361-1378.
  • 5
    • 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. Rational Mech. Anal., 82 (1983), 313-345.
    • (1983) Arch. Rational Mech. Anal , vol.82 , pp. 313-345
    • Berestycki, H.1    Lions, P.L.2
  • 6
    • 0002449782 scopus 로고
    • Minimum action solutions of some vector field equations
    • H. Brezis and E. Lieb, Minimum action solutions of some vector field equations, Comm. Math. Phys., 96 (1984), 97-113.
    • (1984) Comm. Math. Phys , vol.96 , pp. 97-113
    • Brezis, H.1    Lieb, E.2
  • 7
    • 77249086636 scopus 로고    scopus 로고
    • Symmetry and monotonicity of least energy solutions, Calc. Var. Partial Diff. Equations
    • in press
    • J. Byeon, L. Jeanjean and M. Maris, Symmetry and monotonicity of least energy solutions, Calc. Var. Partial Diff. Equations, in press.
    • Byeon, J.1    Jeanjean, L.2    Maris, M.3
  • 8
    • 0001394174 scopus 로고    scopus 로고
    • Theory of incoherent self-focusing in biased photorefractive media
    • D. N. Christodoulides, T. H. Coskun, M. Mitchell and M. Segev, Theory of incoherent self-focusing in biased photorefractive media, Phys. Rev. Lett., 78 (1997), 646-649.
    • (1997) Phys. Rev. Lett , vol.78 , pp. 646-649
    • Christodoulides, D.N.1    Coskun, T.H.2    Mitchell, M.3    Segev, M.4
  • 9
    • 33646561146 scopus 로고    scopus 로고
    • On the existence and regularity of ground states for a nonlinear system of coupled Schrödinger equations
    • R. Cipolatti and W. Zumpichiatti, On the existence and regularity of ground states for a nonlinear system of coupled Schrödinger equations, Comput. Appl. Math., 18(1999), 19-36.
    • (1999) Comput. Appl. Math , vol.18 , pp. 19-36
    • Cipolatti, R.1    Zumpichiatti, W.2
  • 10
    • 0034299686 scopus 로고    scopus 로고
    • Orbitally stable standing waves for a system of coupled nonlinear Schrödinger equations
    • R. Cipolatti and W. Zumpichiatti, Orbitally stable standing waves for a system of coupled nonlinear Schrödinger equations, Nonlinear Anal., 42 (2000), 445-461.
    • (2000) Nonlinear Anal , vol.42 , pp. 445-461
    • Cipolatti, R.1    Zumpichiatti, W.2
  • 11
    • 0000995516 scopus 로고
    • Action minima amoung solutions to a class of euclidean scalar field equations
    • S. Coleman, V. Glaser and A. Martin, Action minima amoung solutions to a class of euclidean scalar field equations, Commun. Math. Phys., 58 (1978), 211-221.
    • (1978) Commun. Math. Phys , vol.58 , pp. 211-221
    • Coleman, S.1    Glaser, V.2    Martin, A.3
  • 12
    • 36349026597 scopus 로고    scopus 로고
    • On the blow-up threshold for weakly coupled nonlinear Schrödinger equations
    • L. Fanelli and E. Montefusco, On the blow-up threshold for weakly coupled nonlinear Schrödinger equations, J. Phys. A: Math. Theor., 40 (2007), 14139-14150.
    • (2007) J. Phys. A: Math. Theor , vol.40 , pp. 14139-14150
    • Fanelli, L.1    Montefusco, E.2
  • 14
    • 42949129991 scopus 로고    scopus 로고
    • Multiple existence of solutions for coupled nonlinear Schrödinger equations
    • N. Hirano and N. Shioji, Multiple existence of solutions for coupled nonlinear Schrödinger equations, Nonlinear Anal., 68 (2008), 3845-3859.
    • (2008) Nonlinear Anal , vol.68 , pp. 3845-3859
    • Hirano, N.1    Shioji, N.2
  • 16
    • 20144365508 scopus 로고    scopus 로고
    • A positive solution for a nonlinear Schrödinger equation on ℝN
    • L. Jeanjean and K. Tanaka, A positive solution for a nonlinear Schrödinger equation on ℝN, Indiana Univ. Math. J., 54 (2005), 443-464.
    • (2005) Indiana Univ. Math. J , vol.54 , pp. 443-464
    • Jeanjean, L.1    Tanaka, K.2
  • 17
    • 0019478360 scopus 로고
    • Polarization in optical fibers
    • I.P. Kaminow, Polarization in optical fibers, IEEE J. Quantum Electron., 17 (1981), 15-22.
    • (1981) IEEE J. Quantum Electron , vol.17 , pp. 15-22
    • Kaminow, I.P.1
  • 19
    • 18844402155 scopus 로고    scopus 로고
    • Spikes in two coupled nonlinear Schrödinger equations
    • T. C. Lin and J. Wei, Spikes in two coupled nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 403-439.
    • (2005) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.22 , pp. 403-439
    • Lin, T.C.1    Wei, J.2
  • 20
    • 33846096848 scopus 로고    scopus 로고
    • Symbiotic bright solitary wave solutions of coupled nonlinear Schrödinger equations
    • T. C. Lin and J. Wei, Symbiotic bright solitary wave solutions of coupled nonlinear Schrödinger equations, Nonlinearity, 19 (2006), 2755-2773.
    • (2006) Nonlinearity , vol.19 , pp. 2755-2773
    • Lin, T.C.1    Wei, J.2
  • 21
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variation. The locally compact case. Part I
    • P. L. Lions, The concentration-compactness principle in the calculus of variation. The locally compact case. Part I, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 1 (1984), 109-145.
    • (1984) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.1 , pp. 109-145
    • Lions, P.L.1
  • 22
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variation. The locally compact case. Part II
    • P. L. Lions, The concentration-compactness principle in the calculus of variation. The locally compact case. Part II, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 1 (1984), 223-283.
    • (1984) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.1 , pp. 223-283
    • Lions, P.L.1
  • 23
    • 33747158213 scopus 로고    scopus 로고
    • Positive solutions for a weakly coupled nonlinear Schrödinger system
    • L. A. Maia, E. Montefusco and B. Pellacci, Positive solutions for a weakly coupled nonlinear Schrödinger system, J. Differential Equations, 229 (2006), 743-767.
    • (2006) J. Differential Equations , vol.229 , pp. 743-767
    • Maia, L.A.1    Montefusco, E.2    Pellacci, B.3
  • 24
    • 67651109532 scopus 로고    scopus 로고
    • Orbital stability of ground state solutions of coupled nonlinear Schrödinger equations
    • preprint
    • L. A. Maia, E. Montefusco and B. Pellacci, Orbital stability of ground state solutions of coupled nonlinear Schrödinger equations, preprint.
    • Maia, L.A.1    Montefusco, E.2    Pellacci, B.3
  • 25
    • 0023293392 scopus 로고
    • Nonlinear pulse propagation in birefringence optical fiber
    • C. R. Menyuk, Nonlinear pulse propagation in birefringence optical fiber, IEEE J. Quantum Electron., 23 (1987), 174-176.
    • (1987) IEEE J. Quantum Electron , vol.23 , pp. 174-176
    • Menyuk, C.R.1
  • 26
    • 0024914687 scopus 로고
    • Pulse propagation in an elliptically birefringent Kerr medium
    • C. R. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium, IEEE J. Quantum Electron., 25 (1989), 2674-2682.
    • (1989) IEEE J. Quantum Electron , vol.25 , pp. 2674-2682
    • Menyuk, C.R.1
  • 27
    • 36349003376 scopus 로고    scopus 로고
    • Semiclassical states for weakly coupled nonlinear Schrödinger syste
    • E. Montefusco, B. Pellacci and M. Squassina, Semiclassical states for weakly coupled nonlinear Schrödinger syste, J. Eur. Math. Soc., 10 (2008), 47-71.
    • (2008) J. Eur. Math. Soc , vol.10 , pp. 47-71
    • Montefusco, E.1    Pellacci, B.2    Squassina, M.3
  • 28
    • 33646567490 scopus 로고    scopus 로고
    • Coupled nonlinear Schrödinger systems with potentials
    • A. Pomponio, Coupled nonlinear Schrödinger systems with potentials, J. Differential Equations, 227 (2006), 258-281.
    • (2006) J. Differential Equations , vol.227 , pp. 258-281
    • Pomponio, A.1
  • 30
    • 50249093316 scopus 로고    scopus 로고
    • Radial solutions and phase separation in a system of two coupled Schrödinger equations
    • J. Wei and T. Weth, Radial solutions and phase separation in a system of two coupled Schrödinger equations, Arch. Ration. Mech. Anal., 190 (2008), 83-106.
    • (2008) Arch. Ration. Mech. Anal , vol.190 , pp. 83-106
    • Wei, J.1    Weth, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.