Pascal Bégout, “Maximum decay rate for finite-energy solutions of nonlinear Schrödinger equations”, Differential and Integral Equations, vol. 17, n. 11, 2004, pp. 1411–1422.
We give explicit time lower bounds in the Lebesgue spaces for all nontrivial solutions of nonlin-ear Schrodinger equations bounded in the energy space. The result applies for these equations setin any domain ofRN;including the whole space. This also holds for a large class of nonlinearities,thereby extending the results obtained by Hayashi and Ozawa in  and by the author in .