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Nonlinear Schrödinger evolution equations. (English) Zbl 0451.35023

MSC:
35J10 Schrödinger operator, Schrödinger equation
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] Baillon, J.B.; Cazenave, T.; Figueira, M., Equation de Schrödinger nonlinéare, C.r. acad. sci., Paris, 284, 869-872, (1977) · Zbl 0349.35048
[2] C{\scAZENAVE} T., Equations de Schrödinger nonlinéares, Proc. Roy. Edinburgh (to appear).
[3] J. G{\scINIBRE} & V{\scELO} G., on a class of nonlinear Schrödinger equations.
[4] Glassey, R.T., On the blowing up of solutions to the Cauchy problem for the nonlinear Schrödinger equation, J. math. phys., 18, 1794-1979, (1977) · Zbl 0372.35009
[5] Lin, J.E.; Strauss, W.A., Decay and scattering of solutions of a nonlinear schrd̈inger equation, J. funct. anal., 30, 245-263, (1978) · Zbl 0395.35070
[6] Nirenberg, L., On elliptic partial differential equations, Ann. sci. norm. sup. Pisa, 13, 115-162, (1959) · Zbl 0088.07601
[7] Segal, I., Nonlinear semi-groups, Ann. math., 78, 339-364, (1963) · Zbl 0204.16004
[8] Strauss, W.A., The nonlinear Schrödinger equation, (), 452-465
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