EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 5 / No 4 (2010) Math. Model. Nat. Phenom., 5 4 (2010) 448-469 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 448 - 469
DOI https://doi.org/10.1051/mmnp/20105417
Published online 12 May 2010
  1. S. Adachi. A Positive solution of a nonhomogeneous elliptic equation in RN with G-invariant nonlinearity. Comm. PDE., 27 (2002), No. 1-2, 1–22. [CrossRef] [Google Scholar]
  2. V. Bach, J. Fröhlich, I.M. Sigal. Renormalization group analysis of spectral problems in quantum field theory. Adv. Math., 137 (1998), No. 2, 205–298. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Berestycki, P.-L. Lions. Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), No. 4, 313–345. [MathSciNet] [Google Scholar]
  4. H. Berestycki, P.-L. Lions. Nonlinear scalar field equations. II. Existence of infinitely many solutions. Arch. Rational Mech. Anal., 82 (1983), No. 4, 347–375. [MathSciNet] [Google Scholar]
  5. H. Berestycki, P.-L. Lions, L. Peletier. An ODE approach to the existence of positive solutions for semilinear problems in ℝN. Indiana Univ. Math. J., 30 (1981), No. 1, 141–157. [CrossRef] [MathSciNet] [Google Scholar]
  6. V.S. Buslaev, G.S. Perelman. Scattering for the nonlinear Schrödinger equation: states that are close to a soliton. St. Petersburg Math. J., 4 (1993), No. 6, 1111–1142. [MathSciNet] [Google Scholar]
  7. V.S. Buslaev, C. Sulem. On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Ann. Inst. H. Poincare Anal. Non Lineaire, 20 (2003), No. 3, 419–475 [Google Scholar]
  8. S. Cuccagna. On asymptotic stability of ground states of NLS, Rev. Math. Phys., 15 (2003), No. 8, 877–903. [CrossRef] [MathSciNet] [Google Scholar]
  9. S.-M. Chang, S. Gustafson, K. Nakanishi, T.-P. Tsai. Spectra of linearized operators for NLS solitary waves. SIAM J. Math. Anal., 39 (2007), No. 4, 1070–1111. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Cuccagna, D. Pelinovsky. Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear Schrödinger problem. J. Math. Phys., 46 (2005), No. 5, 053520, 15 pp. [Google Scholar]
  11. B. Erdogan, W. Schlag. Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II. J. Anal. Math., 99 (2006), 199–248. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Floer, A. Weinstein. Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. Funct. Anal., 69 (1986), No. 3, 397–408. [CrossRef] [MathSciNet] [Google Scholar]
  13. S. Cuccagna, D. Pelinovsky, V. Vougalter. Spectra of positive and negative energies in the linearized NLS problem. Comm. Pure Appl. Math., 58 (2005), No. 1, 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Grillakis. Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system. Comm. Pure Appl. Math., 43 (1990), No. 3, 299–333. [CrossRef] [MathSciNet] [Google Scholar]
  15. S. Gustafson, I.M. Sigal. Mathematical concepts of quantum mechanics. Springer–Verlag, Berlin, 2003. [Google Scholar]
  16. Z. Gang, I.M. Sigal. Asymptotic stability of nonlinear Schrödinger equations with potential, Rev. Math. Phys., 17 (2005), No. 10, 1143–1207. [CrossRef] [MathSciNet] [Google Scholar]
  17. P.D. Hislop, I.M. Sigal. Introduction to spectral theory with applications to Schrödinger operators. Springer, 1996. [Google Scholar]
  18. T. Kapitula, B. Sandstede. Edge bifurcations for near integrable systems via Evans functions techniques. SIAM J. Math.Anal., 33 (2002), No. 5, 1117–1143. [Google Scholar]
  19. T. Kapitula, B. Sandstede. Eigenvalues and resonances using the Evans functions. Discrete Contin. Dyn. Syst., 10 (2004), No. 4, 857–869. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Klaus, B. Simon. Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case. Ann. Phys., 130 (1980), No. 2, 251–281. [CrossRef] [Google Scholar]
  21. E. Lieb, M. Loss. Analysis. Graduate studies in Mathematics, 14. American Mathematical Society, Providence, 1997. [Google Scholar]
  22. E.Lieb, B.Simon, A. Wightman. Book “Studies in mathematical physics: Essays in Honor of Valentine Bargmann.” Princeton University Press, 1976. [Google Scholar]
  23. K. McLeod. Uniqueness of positive radial solutions of Δu +f(u) = 0 in Rn. II. Trans. Amer. Math. Soc., 339 (1993), No. 2, 495–505. [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Pelinovsky, Y. Kivshar, V. Afanasjev. Internal modes of envelope solitons, Phys. D, 116 (1998), No. 1–2, 121–142. [Google Scholar]
  25. G. Perelman. Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations. Comm. Partial Differential Equations, 29 (2004), No. 7–8, 1051–1095. [CrossRef] [MathSciNet] [Google Scholar]
  26. W. Strauss. Existence of solitary waves in higher dimensions. Comm.Math.Phys., 55 (1977), No. 2, 149–162. [Google Scholar]
  27. B.Simon. Functional integration and quantum physics. Pure and Applied Mathematics, 86 (1979), Academic Press. [Google Scholar]
  28. W. Schlag. Stable manifolds for an orbitally unstable nonlinear Schrödinger equation. Ann. of Math. (2), 169 (2009), No. 1, 139–227. [CrossRef] [MathSciNet] [Google Scholar]
  29. V. Vougalter. On the negative index theorem for the linearized NLS problem. To appear in Canad. Math. Bull. [Google Scholar]
  30. V. Vougalter, D. Pelinovsky. Eigenvalues of zero energy in the linearized NLS problem. J. Math. Phys., 47 (2006), No. 6, 062701, 13 pp. [Google Scholar]
  31. M.I. Weinstein. Modulation stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal., 16 (1985), No. 3, 472–491. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.