메뉴 건너뛰기




Volumn 12, Issue 3, 2012, Pages 639-658

On the orbital stability of standing-wave solutions to a coupled non-linear Klein-Gordon equation

Author keywords

Elliptic systems; Orbital stability; Standing waves; Unbounded domain

Indexed keywords


EID: 84867752507     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2012-0311     Document Type: Article
Times cited : (29)

References (30)
  • 1
    • 0344981531 scopus 로고    scopus 로고
    • Existence and stability of ground-state solutions of a Schrödinger-KdV system
    • J. ALBERT AND J. ANGULO PAVA, Existence and stability of ground-state solutions of a Schrödinger-KdV system, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), pp. 987-1029.
    • (2003) Proc. Roy. Soc. Edinburgh Sect. A , vol.133 , pp. 987-1029
    • Albert, J.1    Angulo Pava, J.2
  • 2
    • 0004235774 scopus 로고
    • of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge Corrected reprint of the 1993 original
    • A. AMBROSETTI AND G. PRODI, A primer of Nonlinear Analysis, vol. 34 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1993. Corrected reprint of the 1993 original.
    • (1993) A Primer of Nonlinear Analysis , vol.34
    • Ambrosetti, A.1    Prodi, G.2
  • 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), pp. 313-345.
    • (1983) Arch. Rational Mech. Anal. , vol.82 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 6
    • 77955917336 scopus 로고
    • [Collection of Applied Mathematics for the Master's Degree], Masson, Paris Théorie et applications. [Theory and applications]
    • H. BREZIS, Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], Masson, Paris, 1983. Théorie et applications. [Theory and applications].
    • (1983) Analyse Fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise
    • Brezis, H.1
  • 7
    • 0002350320 scopus 로고
    • On space-time means and strong global solutions of nonlinear hyperbolic equations
    • P. BRENNER, On space-time means and strong global solutions of nonlinear hyperbolic equations, Math. Z. 201 (1989), pp. 45-55.
    • (1989) Math. Z. , vol.201 , pp. 45-55
    • Brenner, P.1
  • 8
    • 47849085259 scopus 로고    scopus 로고
    • Interacting Q-balls
    • Y. BRIHAYE AND B. HARTMANN, Interacting Q-balls, Nonlinearity 21 (2008), pp. 1937-1952.
    • (2008) Nonlinearity , vol.21 , pp. 1937-1952
    • Brihaye, Y.1    Hartmann, B.2
  • 9
    • 84945016371 scopus 로고
    • Minimal rearrangements of Sobolev functions
    • J. E. BROTHERS AND W. P. ZIEMER, Minimal rearrangements of Sobolev functions, J. Reine Angew. Math. 384 (1988), pp. 153-179.
    • (1988) J. Reine Angew. Math. , vol.384 , pp. 153-179
    • Brothers, J.E.1    Ziemer, W.P.2
  • 10
    • 0002342492 scopus 로고    scopus 로고
    • Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems
    • J. BYEON, Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Differential Equations 163 (2000), pp. 429-474.
    • (2000) J. Differential Equations , vol.163 , pp. 429-474
    • Byeon, J.1
  • 11
    • 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
  • 14
    • 0000890194 scopus 로고
    • The global Cauchy problem for the nonlinear Klein-Gordon equation
    • J. GINIBRE AND G. VELO, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985), pp. 487-505.
    • (1985) Math. Z. , vol.189 , pp. 487-505
    • Ginibre, J.1    Velo, G.2
  • 15
    • 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
  • 16
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry. II
    • 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
  • 18
    • 84867786306 scopus 로고    scopus 로고
    • of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, second ed.
    • E. H. LIEB AND M. LOSS, Analysis, vol. 14 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, second ed., 2001.
    • (2001) Analysis , vol.14
    • Lieb, E.H.1    Loss, M.2
  • 19
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case. II
    • P.-L. LIONS, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), pp. 223-283.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 223-283
    • Lions, P.-L.1
  • 20
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case. II
    • The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), pp. 223-283.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 223-283
  • 21
    • 84867820519 scopus 로고    scopus 로고
    • Orbital stability of solitary waves for a nonlinear Schrödinger system
    • N. V. NGUYEN AND Z.-Q. WANG, Orbital stability of solitary waves for a nonlinear Schrödinger system, Adv. Differential Equations 16 (2011), pp. 977-1000.
    • (2011) Adv. Differential Equations , vol.16 , pp. 977-1000
    • Nguyen, N.V.1    Wang, Z.-Q.2
  • 22
    • 0039810296 scopus 로고
    • Abstract non-linear wave equations
    • Springer-Verlag, Berlin
    • M. REED, Abstract Non-Linear Wave Equations, Lecture Notes in Mathematics, Vol. 507, Springer-Verlag, Berlin, 1976.
    • (1976) Lecture Notes in Mathematics , vol.507
    • Reed, M.1
  • 23
    • 0001418965 scopus 로고
    • Non-linear semi-groups
    • I. SEGAL, Non-linear semi-groups, Ann. of Math. (2) 78 (1963), pp. 339-364.
    • (1963) Ann. of Math. , vol.78 , Issue.2 , pp. 339-364
    • Segal, I.1
  • 24
    • 0001420204 scopus 로고
    • Instability of nonlinear bound states
    • J. SHATAH AND W. STRAUSS, Instability of nonlinear bound states, Comm. Math. Phys. 100 (1985), pp. 173-190.
    • (1985) Comm. Math. Phys. , vol.100 , pp. 173-190
    • Shatah, J.1    Strauss, W.2
  • 25
    • 0003482633 scopus 로고
    • of CBMS Regional Conference Series in Mathematics, Published for the Conference Board of the Mathematical Sciences, Washington, DC
    • W. A. STRAUSS, Nonlinear Wave Equations, vol. 73 of CBMS Regional Conference Series in Mathematics, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1989.
    • (1989) Nonlinear Wave Equations , vol.73
    • Strauss, W.A.1
  • 26
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • G. TALENTI, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110 (1976), pp. 353-372.
    • (1976) Ann. Mat. Pura Appl. , vol.110 , Issue.4 , pp. 353-372
    • Talenti, G.1
  • 27
    • 84867781444 scopus 로고    scopus 로고
    • of CBMS Regional Conference Series in Mathematics, Published for the Conference Board of the Mathematical Sciences, Washington, DC Local and global analysis
    • T. TAO, Nonlinear Dispersive Equations, vol. 106 of CBMS Regional Conference Series in Mathematics, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 2006. Local and global analysis.
    • (2006) Nonlinear Dispersive Equations , vol.106
    • Tao, T.1
  • 28
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • M. I. WEINSTEIN, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39 (1986), pp. 51-67.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 51-67
    • Weinstein, M.I.1
  • 29
    • 0037427987 scopus 로고    scopus 로고
    • On the standing wave in coupled non-linear Klein-Gordon equations
    • J. ZHANG, On the standing wave in coupled non-linear Klein-Gordon equations, Math. Methods Appl. Sci. 26 (2003), pp. 11-25.
    • (2003) Math. Methods Appl. Sci. , vol.26 , pp. 11-25
    • Zhang, J.1
  • 30
    • 77953728644 scopus 로고    scopus 로고
    • Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations
    • J. ZHANG, Z.-H. GAN, AND B.-L. GUO, Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations, Acta Math. Appl. Sin. Engl. Ser. 26 (2010), pp. 427-442.
    • (2010) Acta Math. Appl. Sin. Engl. Ser. , vol.26 , pp. 427-442
    • Zhang, J.1    Gan, Z.-H.2    Guo, B.-L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.