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On a class of non linear Schrödinger equations with non local interactions. (English) Zbl 0407.35063

MSC:
35P25 Scattering theory for PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
47J05 Equations involving nonlinear operators (general)
81U99 Quantum scattering theory
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References:
[1] Baillon, J.B., Cazenave, T., Figueira, M.: Equation de Schrödinger non linéaire. C.R. Acad. Sci. Paris, Sér. A284, 869-872 (1977) · Zbl 0349.35048
[2] Friedman, A.: Partial differential equations. New York: Holt, Rinehart & Winston, 1969 · Zbl 0224.35002
[3] Ginibre, J., Velo, G.: On a class of non linear Schrödinger equations I. The Cauchy problem, general case. J. Functional Analysis32, 1-32 (1979). II. Scattering theory, general case. J. Functional Analysis32, 33-71 (1979). III. Special theories in dimensions 1, 2 and 3. Ann. Inst. H. Poincaré, Sect. A28, 287-316 (1978) · Zbl 0396.35028 · doi:10.1016/0022-1236(79)90076-4
[4] Ginibre, J., Velo, G.: The classical field limit of scattering theory for non relativistic many boson systems. Comm. Math. Phys.66, 37-76 (1979) · Zbl 0443.35067 · doi:10.1007/BF01197745
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[6] Lin, J.E., Strauss, W.: Decay and Scattering of Solutions of a non linear Schrödinger Equation. J. Functional Analysis30, 245-263 (1978) · Zbl 0395.35070 · doi:10.1016/0022-1236(78)90073-3
[7] Pecher, H., von Wahl, W.: Time dependent non linear Schrödinger equations. Manuscripta Math. (to appear) · Zbl 0399.35030
[8] Strauss, W.: The non linear Schrödinger equation. In: Proceedings of a Conference on Continuum Mechanics and Partial Differential Equations (Rio de Janeiro (1977), pp. 452-465. Amsterdam-New York-Oxford: North Holland 1978
[9] Bove, A., Da Prato, G., Fano, G.: An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction. Comm. Math. Phys.37, 183-191 (1974); On the Hartree-Fock time-dependent problem, Comm. Math. Phys.49, 25-33 (1976) · Zbl 0303.34046 · doi:10.1007/BF01646344
[10] Chadam, J., Glassey, R.T.: Global existence of solutions to the Cauchy problem for time dependent Hartree equations. J. Mathematical Phys.16, 1122-1130 (1975). Glassey, R.T.: Asymptotic behaviour of solutions to certain Nonlinear Schrödinger Hartree equations. Comm. Math. Phys.53, 9-18 (1977) · Zbl 0299.35084 · doi:10.1063/1.522642
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