Global existence and blow up of solutions for the inhomogeneous nonlinear Schrödinger equation in R2

Journal of Mathematical Analysis and Applications

Volumn 338, Issue 2, 2008, Pages 1008-1019

  Wang, Yanjin ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Blow up; Global existence; Inhomogeneous nonlinearity; Schr dinger equation

Indexed keywords

EID: 34848840950     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.05.057     Document Type: Article

References (19)

1. Adams R.A., and Fournier J. Cone conditions and properties of Sobolev spaces. J. Math. Anal. Appl. 61 (1977) 713-734
2. Akhmediev N.N. Novel class of nonlinear surfaces waves: Asymmetric modes in a symmetric layered structure. Sov. Phys. JETP 56 (1982) 299-303
3. Berestycki H., Gallouët T., and Kavian O. Èquations de champs scalaires euclidiens non linèaires dans le plan. C. R. Math. Acad. Sci. Paris Sèr. I 297 (1983) 307-310
4. Berestycki H., and Lions P.L. Nonlinear scalar field equations. I. Existence of a ground state. Arch. Ration. Mech. Anal. 82 (1983) 313-345
5. Cazenave T. Semilinear Schrödinger Equations. Courant Lect. Notes Math. vol. 10 (2003), New York University, New York
6. de Bouard A., and Fukuizumi R. Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities. Ann. Henri Poincaré 6 (2005) 1157-1177
7. Fibich G., and Wang X.P. Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities. Phys. D 175 (2003) 96-108
8. Fukuizumi R., and Ohta M. Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities. J. Math. Kyoto Univ. 45 (2005) 145-158
9. Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in the presence of symmetry I. J. Funct. Anal. 74 (1987) 160-197
10. Jones C.K.R.T. Instability of standing waves for nonlinear Schrödinger-type equations. Ergodic Theory Dynam. Systems 8 (1988) 119-138
11. Kato T. On nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Phys. Théor. 46 (1987) 113-129
12. Kato T. Nonlinear Schrödinger equations. Schrödinger Operators. Sønderborg, 1988. Lect. Notes Phys. Monogr. vol. 345 (1989), Springer, Berlin 218-263
13. Liu C.S., and Tripathi V.K. Laser guiding in an axially nonuniform plasma channel. Phys. Plasmas 1 (1994) 3100-3103
14. Liu Y., Wang X., and Wang K. Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity. Trans. Amer. Math. Soc. 358 (2006) 2105-2122
15. N. Ann. Inst. H. Poincaré Phys. Théor. 64 (1996) 33-85
16. Pang P.Y.H., Wang H., and Wang Y. Blow-up solutions of inhomogeneous nonlinear Schrödinger equations. Calc. Var. Partial Differential Equations 26 (2006) 137-169
17. Weinstein M.I. Nonlinear Schrödinger equations and sharp interpolation estimates. Comm. Math. Phys. 87 (1983) 567-576
18. Zhang J. Stability of attractive Bose-Einstein condensates. J. Stat. Phys. 101 (2000) 731-746
19. Zhang J. Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations. Nonlinear Anal. 48 (2002) 191-207