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Decay and scattering of solutions of a nonlinear Schrödinger equation. (English) Zbl 0395.35070


MSC:

35P25 Scattering theory for PDEs
47A10 Spectrum, resolvent
35Q99 Partial differential equations of mathematical physics and other areas of application
35G25 Initial value problems for nonlinear higher-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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References:

[1] {\scJ. Ginibre and G. Velo}, On a class of nonlinear Schrödinger equations, preprint. · Zbl 0396.35029
[2] Lin, J.E., Time decay of two conservative equations, ()
[3] Morawetz, C.S., Notes on time decay and scattering for some hyperbolic problems, (1975), SIAM · Zbl 0303.35002
[4] Morawetz, C.S.; Strauss, W.A., Decay and scattering of solutions of a nonlinear relativistic wave equation, Comm. pure appl. math., 25, 1-31, (1972) · Zbl 0228.35055
[5] Pecher, H., Das verhalten globaler Lösungen nichtlinearer wellengleichungen für Grosse zeiten, () · Zbl 0265.35051
[6] Reed, M., Abstract non-linear wave equations, () · Zbl 0317.35002
[7] Segal, I.E., Nonlinear semigroups, Ann. of math., 78, 339-364, (1963)
[8] Strauss, W.A., On weak solutions of semi-linear hyperbolic equations, An. acad. brasil ci., 42, 645-651, (1970) · Zbl 0217.13104
[9] Strauss, W.A., Nonlinear scattering theory, (), 53-78 · Zbl 0297.35062
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