Scattering theory for Hartree type equations

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1. [1] J.E. Barab, Nonexistence of asymptotic free solutions for a nonlinear Schrödinger equation. J. Math. Phys., t. 25, 1984, p. 3270-3273. Zbl0554.35123MR761850
2. [2] P. Brenner, On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations. Math. Z., t. 186, 1984, p. 383-391. Zbl0524.35084MR744828
3. [3] P. Brenner, On scattering and everywhere defined scattering operators for non–linear Klein-Gordon equations. J. Differential Equations, t. 56, 1985, p. 310-344. Zbl0513.35066MR780495
4. [4] J.M. Chadam and R.T. Glassey, Global existence of solutions to the Cauchy problem for time dependent Hartree equations. J. Math. Phys., t. 16, 1975, p. 1122-1130. Zbl0299.35084MR413843
5. [5] A. Friedman, Partial Differential Equations. Holt-Rinehart and Winston, New York, 1969. Zbl0224.35002MR445088
6. [6] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equation 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. Zbl0397.35012MR533219
7. [7] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations with non local interactin. Math. Z., t. 170, 1980, p. 109-136. Zbl0407.35063MR562582
8. [8] J. Ginibre and G. Velo, Sur une équation de Schrödinger non linéaire avec interaction non locale, in Nonlinear partial differential equations and their applications. Collège de France, Séminaire, vol. II, Pitman, Boston, 1981. Zbl0497.35024MR652511
9. [9] J. Ginibre and G. Velo, Scattering theory in the energy space for a class of non–linear Schrödinger equations, J. Math. pures et appl., t. 64, 1985, p. 363-401. Zbl0535.35069MR839728
10. [10] R.T. Glassey, Asymptotic behavior of solutions to a certain nonlinear-Hartree equations, Comm. Math. Phys., t. 53, 1977, p. 9-18. Zbl0339.35013MR486956
11. [11] N. Hayashi and M. Tsutsumi, L∞-decay of classical solutions for nonlinear Schrödinger equations, preprint. Zbl0651.35014
12. [12] N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations, to appear in J. Funct. Anal. Zbl0657.35033MR880978
13. [13] N. Hayashi and Y. Tsutsumi, Remarks on the scattering problem for nonlinear Schrödinger equations, preprint. MR921265
14. [14] W. Hunziker, On the space-time behavior of Schrödinger wavefunctions. J. Math. Phys., t. 7, 1965, p. 300-304. Zbl0151.43801MR193939
15. [15] A. Jensen, Commutator methods and a smoothing property of the Schrödinger evolution group. Math. Z., t. 191, 1986, p. 53-59. Zbl0594.35032MR812602
16. [16] E.M. Stein, Singular Integral and Differentiability Properties of Functions, Princeton Univ. Press. Princeton Math. Series30, 1970. Zbl0207.13501MR290095
17. [17] W.A. Strauss, Nonlinear invariant wave equations, in Invariant Wave Equations (Erice, 1977), Lecture Notes in Physics, t. 78, Springer-Verlag, Berlin-Heidelberg- New York, 1978, p. 197-249. MR498955
18. [18] W.A. Strauss, Nonlinear scattering theory at low energy. J. Funct. Anal., t. 41, 1981, p. 110-133. Zbl0466.47006MR614228
19. [19] W.A. Strauss, Nonlinear Scattering theory at low energy: Sequel. J. Funct. Anal., t. 43, p. 281-293, Zbl0494.35068MR636702
20. [20] R.S. Strichartz, Restrictions of Fourier Transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J., t. 44, 1977, p. 705-714. Zbl0372.35001MR512086
21. [21] Y. Tsutsumi, Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations, Doctor Thesis, Univ. of Tokyo, 1985. 
22. [22] Y. Tsutsumi, Scattering problem for nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Physique Théorique, t. 43, 1985, p. 321-347. Zbl0612.35104MR824843
23. [23] Y. Tsutsumi and K. Yajima, The asymptotic behavior of nonlinear Schrödinger equations, Bull. (New Series). Amer. Math. Soc., t. 11, 1984, p. 186-188. Zbl0555.35028MR741737
24. [24] K. Yajima, The surfboard Schrödinger equations. Comm. Math. Phys., t. 96, 1984, p. 349-360. Zbl0599.35037MR769352
25. [25] J. Ginibre, Private communication. 
26. [26] T. Kato, On nonlinear Schrödinger equations, preprint, University of California, Berkeley, 1986. MR1037322
27. [27] Y. Tsutsumi, L2-solutions for nonlinear Schrödinger equations and nonlinear groups, to appear in Funkcialaj Ekvacioj. Zbl0638.35021MR915266

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