Scattering theory in the weighted L 2 (ℝ n ) spaces for some Schrödinger equations
Hayashi, Nakao ; Ozawa, Tohru
Annales de l'I.H.P. Physique théorique, Tome 49 (1988), p. 17-37 / Harvested from Numdam
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Publié le : 1988-01-01
@article{AIHPA_1988__48_1_17_0,
     author = {Hayashi, Nakao and Ozawa, Tohru},
     title = {Scattering theory in the weighted $L^2 (\mathbb {R}^n)$ spaces for some Schr\"odinger equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {49},
     year = {1988},
     pages = {17-37},
     mrnumber = {947158},
     zbl = {0659.35078},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1988__48_1_17_0}
}

Hayashi, Nakao; Ozawa, Tohru. Scattering theory in the weighted $L^2 (\mathbb {R}^n)$ spaces for some Schrödinger equations. Annales de l'I.H.P. Physique théorique, Tome 49 (1988) pp. 17-37. http://gdmltest.u-ga.fr/item/AIHPA_1988__48_1_17_0/

[1] J.E. Barab, Nonexistence of asymptotic free solutions for a nonlinear Schrödinger equation. J. Math. Phys., t. 25, 1984, p. 3270-3273. | MR 761850 | Zbl 0554.35123

[2] J. Bergh and J. Löfström, Interpolation Spaces. Berlin, Heidelberg, New York, Springer, 1976. | MR 482275 | Zbl 0344.46071

[3] A. Friedman, Partial Differential Equations. Holt-Rinehart and Winston, New York, 1969. | MR 445088 | Zbl 0224.35002

[4] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations I, II. J. Funct. Anal., t. 32, 1979, p. 1-32, 33-71; III. Ann. Inst. Henri Poincaré, Physique Théorique, t. 28, 1978, p. 287-316. | Numdam | MR 533219 | Zbl 0396.35028

[5] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of nonlinear Schrödinger equations. J. Math. pures et appl., t. 64, 1985, p. 363-401. | MR 839728 | Zbl 0535.35069

[6] J. Ginibre and G. Velo, Private communication.

[7] N. Hayashi and Y. Tsutsumi, Scattering theory for Hartree type equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 46, 1987, p. 187-213. | Numdam | MR 887147 | Zbl 0634.35059

[8] N. Hayashi and Y. Tsutsumi, Remarks on the scattering problem for nonlinear Schrödinger equations, to appear in the Proceedings of UAB conference on Differential Equations and Mathematical Physics, Springer-Verlag, New York, 1986. | MR 921265 | Zbl 0633.35059

[9] N. Hayashi and T. Ozawa, Time decay of solutions to the Cauchy problem for time-dependent Schrödinger-Hartree equations. Commun. Math. Phys., t. 110, 1987, p. 467-478. | MR 891948 | Zbl 0648.35078

[10] N. Hayashi and T. Ozawa, Smoothing effectfor some Schrödinger equations, preprint RIMS-583, 1987. | MR 1012208

[11] N. Hayashi and T. Ozawa, Time decay for some Schrödinger equations, preprint RIMS-554, 1987. | MR 987581

[12] T. Kato, On nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 46, 1987, p. 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[13] E.M. Stein, Singular Integral and Differentiability Properties of Functions. Princeton Univ. Press, Princeton Math. Series 30, 1970. | MR 290095 | Zbl 0207.13501

[14] W.A. Strauss, Decay and asymptotic for □u = F(u). J. Funct. Anal., t. 2, 1968, p. 409-457. | Zbl 0182.13602

[15] W.A. Strauss, Nonlinear scattering theory at low energy: Sequel. J. Funct. Anal., t. 43, 1981, p. 281-293. | MR 636702 | Zbl 0494.35068

[16] Y. Tsutsumi, Scattering problem for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 43, 1985, p. 321-347. | Numdam | MR 824843 | Zbl 0612.35104

[17] Y. Tsutsumi and K. Yajima, The asymptotic behavior of nonlinear Schrödinger equations. Bull. (New Series), Amer. Math. Soc., t. 11, 1984, p. 186-188. | MR 741737 | Zbl 0555.35028

[18] K. Yajima, Existence of solutions for Schrödinger evolution equations. Commun. Math. Phys., t. 110, 1987, p. 415-426. | MR 891945 | Zbl 0638.35036

[19] J. Ginibre, A remark on some papers by N. Hayashi and T. Ozawa, preprint Or say, 1987.