On nonlinear Schrödinger equations

The Cauchy problem for the nonlinear Schrodinger equation i∂ t u=Δu−F o u, u(0)=φ, on space domain R m , m≥1, is solved under the assumption that F is a C 1 -function (in the real sense)on C itself satisfying F(0)=0 and the growth condition |F'(ξ)≤const|ξ| p−1 , where p 0 On resout le probleme de Cauchy pour l'equation de Schrodinger non lineaire i∂ t u=Δu-F o u, u(0)=φ dans l'espace R m , m≥1, sous l'hypothese que la fonction F est C 1 (au sens reel) de C dans C, et satisfait F(0)=0 et la condition de croissance |F'(ξ)|≤const|ξ| P−1 avec p 0

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