메뉴 건너뛰기




Volumn 366, Issue 1, 2010, Pages 345-359

Stability and instability of standing waves to a system of Schrödinger equations with combined power-type nonlinearities

Author keywords

Coupled Schr dinger system; Ground state; Standing wave solution

Indexed keywords


EID: 75749093908     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.12.011     Document Type: Article
Times cited : (24)

References (29)
  • 1
    • 33644966669 scopus 로고    scopus 로고
    • Bound and ground states of coupled nonlinear Schrödinger equations
    • Ambrosetti A., and Colorado E. Bound and ground states of coupled nonlinear Schrödinger equations. C. R. Math. Acad. Sci. Paris 342 (2006) 453-458
    • (2006) C. R. Math. Acad. Sci. Paris , vol.342 , pp. 453-458
    • Ambrosetti, A.1    Colorado, E.2
  • 2
    • 36348990860 scopus 로고    scopus 로고
    • Standing waves of some coupled nonlinear Schrödinger equations
    • Ambrosetti A., and Colorado E. Standing waves of some coupled nonlinear Schrödinger equations. J. London Math. Soc. 75 (2007) 67-82
    • (2007) J. London Math. Soc. , vol.75 , pp. 67-82
    • Ambrosetti, A.1    Colorado, E.2
  • 3
    • 36349034690 scopus 로고    scopus 로고
    • Note on ground state of nonlinear Schrödinger systems
    • Bartsch T., and Wang Z.Q. Note on ground state of nonlinear Schrödinger systems. J. Partial Differential Equations 19 (2006) 200-207
    • (2006) J. Partial Differential Equations , vol.19 , pp. 200-207
    • Bartsch, T.1    Wang, Z.Q.2
  • 4
    • 0000817006 scopus 로고
    • Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéarires
    • Berestycki H., and Cazenave T. Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéarires. C. R. Acad. Sci. Paris Sér. I 293 (1981) 489-492
    • (1981) C. R. Acad. Sci. Paris Sér. I , vol.293 , pp. 489-492
    • Berestycki, H.1    Cazenave, T.2
  • 5
    • 0020591567 scopus 로고
    • Nonlinear scalar fields equation I. Existence of a ground state
    • Berestycki H., and Lions P.L. Nonlinear scalar fields equation 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
  • 6
    • 0034629612 scopus 로고    scopus 로고
    • Symmetry results for semilinear elliptic systems in the whole space
    • Busca J., and Sirakov B. Symmetry results for semilinear elliptic systems in the whole space. J. Differential Equations 163 (2000) 41-56
    • (2000) J. Differential Equations , vol.163 , pp. 41-56
    • Busca, J.1    Sirakov, B.2
  • 7
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger Equations
    • New York Univ., Courant Inst. Math. Sci., Amer. Math. Soc.
    • Cazenave T. Semilinear Schrödinger Equations. Courant Lect. Notes Math. vol. 10 (2003), New York Univ., Courant Inst. Math. Sci., Amer. Math. Soc.
    • (2003) Courant Lect. Notes Math. , vol.10
    • Cazenave, T.1
  • 9
    • 29144530122 scopus 로고    scopus 로고
    • Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
    • De Bouard A., and Fukuizumi R. Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities. Ann. Henri Poincaré 6 (2005) 1157-1177
    • (2005) Ann. Henri Poincaré , vol.6 , pp. 1157-1177
    • De Bouard, A.1    Fukuizumi, R.2
  • 10
    • 0016092731 scopus 로고
    • On the variational principle
    • Ekeland I. On the variational principle. J. Math. Anal. Appl. 47 (1974) 324-353
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 324-353
    • Ekeland, I.1
  • 12
    • 44449123711 scopus 로고    scopus 로고
    • Schrödinger equations with a spatially decaying nonlinearity: existence and stability of standing waves
    • Genoud F., and Stuart C.A. Schrödinger equations with a spatially decaying nonlinearity: existence and stability of standing waves. Discrete Contin. Dyn. Syst. 21 (2008) 137-186
    • (2008) Discrete Contin. Dyn. Syst. , vol.21 , pp. 137-186
    • Genoud, F.1    Stuart, C.A.2
  • 14
    • 0035641078 scopus 로고    scopus 로고
    • Ground states in non-relativistic quantum electrodynamics
    • Griesemer M., Lieb H.E., and Loss M. Ground states in non-relativistic quantum electrodynamics. Invent. Math. 145 (2001) 557-595
    • (2001) Invent. Math. , vol.145 , pp. 557-595
    • Griesemer, M.1    Lieb, H.E.2    Loss, M.3
  • 15
    • 10944273602 scopus 로고    scopus 로고
    • On the variational approach to the stability of standing waves for the nonlinear Schrödinger equation
    • Hajaiej H., and Stuart C.A. On the variational approach to the stability of standing waves for the nonlinear Schrödinger equation. Adv. Nonlinear Stud. 4 (2004) 469-501
    • (2004) Adv. Nonlinear Stud. , vol.4 , pp. 469-501
    • Hajaiej, H.1    Stuart, C.A.2
  • 18
    • 51249093666 scopus 로고    scopus 로고
    • Uniqueness of ground states of some coupled nonlinear Schrödinger systems and their application
    • Ma L., and Zhao L. Uniqueness of ground states of some coupled nonlinear Schrödinger systems and their application. J. Differential Equations 245 (2008) 2551-2565
    • (2008) J. Differential Equations , vol.245 , pp. 2551-2565
    • Ma, L.1    Zhao, L.2
  • 19
    • 46449120917 scopus 로고    scopus 로고
    • Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system
    • Ma L., and Zhao L. Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system. J. Math. Phys. 49 (2008) 1-17
    • (2008) J. Math. Phys. , vol.49 , pp. 1-17
    • Ma, L.1    Zhao, L.2
  • 20
    • 33747158213 scopus 로고    scopus 로고
    • Positive solutions for a weakly coupled nonlinear Schrödinger system
    • Maia L.A., Montefusco E., and Pellacci B. 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
  • 21
    • 10944249887 scopus 로고    scopus 로고
    • Stability of standing waves for some nonlinear Schrödinger equations
    • McLeod J.B., Stuart C.A., and Troy W.C. Stability of standing waves for some nonlinear Schrödinger equations. Differential Integral Equations 16 (2003) 1025-1038
    • (2003) Differential Integral Equations , vol.16 , pp. 1025-1038
    • McLeod, J.B.1    Stuart, C.A.2    Troy, W.C.3
  • 22
    • 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 (1992) 270-291
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 270-291
    • Rabinowitz, P.H.1
  • 23
    • 33847197945 scopus 로고    scopus 로고
    • Least energy solitary waves for a system of nonlinear Schrödinger equations
    • Sirakov B. Least energy solitary waves for a system of nonlinear Schrödinger equations. Comm. Math. Phys. 271 (2007) 199-221
    • (2007) Comm. Math. Phys. , vol.271 , pp. 199-221
    • Sirakov, B.1
  • 24
    • 75749125092 scopus 로고    scopus 로고
    • Blowup and mass concentration phenomena for a system of Schrödinger equations with combined power-type nonlinearities
    • in revised form, submitted for publication
    • X.F. Song, Blowup and mass concentration phenomena for a system of Schrödinger equations with combined power-type nonlinearities, J. Math. Phys., submitted for publication in revised form
    • J. Math. Phys
    • Song, X.F.1
  • 25
    • 33745665546 scopus 로고    scopus 로고
    • Uniqueness and stability of ground states for some nonlinear Schrödinger equations
    • Stuart C.A. Uniqueness and stability of ground states for some nonlinear Schrödinger equations. J. Eur. Math. Soc. (JEMS) 8 (2006) 399-414
    • (2006) J. Eur. Math. Soc. (JEMS) , vol.8 , pp. 399-414
    • Stuart, C.A.1
  • 26
    • 58149173394 scopus 로고    scopus 로고
    • Lectures on the orbital stability of standing waves and application to the nonlinear Schrödinger equation
    • Stuart C.A. Lectures on the orbital stability of standing waves and application to the nonlinear Schrödinger equation. Milan J. Math. 76 (2008) 329-399
    • (2008) Milan J. Math. , vol.76 , pp. 329-399
    • Stuart, C.A.1
  • 27
    • 34548321243 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation with combined power-type nonlinearities
    • Tao T., Visan M., and Zhang X.Y. The nonlinear Schrödinger equation with combined power-type nonlinearities. Comm. Partial Differential Equations 32 (2007) 1281-1343
    • (2007) Comm. Partial Differential Equations , vol.32 , pp. 1281-1343
    • Tao, T.1    Visan, M.2    Zhang, X.Y.3
  • 29
    • 27944469641 scopus 로고    scopus 로고
    • Sharp threshold for blow-up and global existence in nonlinear Schrödinger equations under a harmonic potential
    • Zhang J. Sharp threshold for blow-up and global existence in nonlinear Schrödinger equations under a harmonic potential. Comm. Partial Differential Equations 30 (2005) 1429-1443
    • (2005) Comm. Partial Differential Equations , vol.30 , pp. 1429-1443
    • Zhang, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.