Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves

Discrete and Continuous Dynamical Systems

Volumn 21, Issue 1, 2008, Pages 137-186

  Genoud, François ^a   Stuart, Charles A ^a  

^a EPFL   (Switzerland)

Author keywords

Bifurcation; Orbital stability; Standing waves

Indexed keywords

EID: 44449123711     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2008.21.137     Document Type: Conference Paper

References (23)

1. A. Ambrosetti and M. Badiale, Variational perturbative methods and bifurcation of bound states from the essential spectrum, Proc Roy. Soc. Edinburgh Sect. A, 128 (1998), 1131-1161.
2. n, Birkhäuser, (2006).
3. A. De Bouard and R. Fukuizumi, Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Ann. Henri Poincaré, 6 (2005), 1157-1177.
4. T. Cazenave, "Semilinear Schrödinger Equations," Courant Lecture Notes in Mathematics, AMS, 2003.
5. T. Cazenave and P.-L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85 (1982), 549-561.
6. S. Chatterji, "Cours D'analyse," Vol. 3, Presses polytechniques et universitaires romandes, 1998.
7. R. Fukuizumi and M. Ohta, Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous potentials, preprint.
8. F. Genoud, PhD Thesis, to appear.
9. D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Second Edition, Springer, 1983.
10. M. Grillakis, J. Shatah and W. Strauss, Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal., 74 (1987), 160-197.
11. H. Hajaiej and C. A. Stuart, On the variational approach to the stability of standing waves for the nonlinear Schrödinger equation, Advanced Nonlinear Studies, 4 (2004), 469-501.
12. P. Hartman, "Ordinary Differential Equations," Birkhauser, 1982.
13. L. Jeanjean and S. Le Coz, An existence and stability result for standing waves of nonlinear Schrödinger equations, Adv. Differential Equations, 11 (2006), 813-840.
14. L. Kantorovitch and G. Akilov, "Analyse Fonctionnelle," Vol. II, Editions Mir, 1981.
15. T. Kato, "Perturbation Theory for Linear Operators," Springer, 1995.
16. S. Kesavan, "Symmetrization and Applications," Series in Analysis, World Scientific, 2006.
17. R. J. Magnus, On the asymptotic properties of solutions to a differential equation in a case of bifurcation without eigenvalues, Proc. Roy. Soc. Edinburgh Sect. A, 104 (1986), 137-159.
18. C. A. Stuart, Bifurcation for Dirichlet problems without eigenvalues, Proc. London Math. Soc. (3), 45 (1982), 169-192.
19. C. A. Stuart, Bifurcation of homoclinic orbits and bifurcation from the essential spectrum, SIAM J. Math. Anal., 20 (1989), 1145-1171.
20. C. A. Stuart, A global branch of solutions to a semilinear equation on an unbounded interval, Proc. Roy. Soc. Edinburgh Sect. A, 101 (1985), 273-282.
21. N) for a semilinear elliptic equation, Proc. London Math. Soc. (3), 57 (1988), 511-541.
22. J. Weidmann, "Spectral Theory of Ordinary Differential Operators," Springer, 1987.
23. n, Arch. Rational Mech. Anal., 115 (1991), 257-274.