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Let u be a nontrivial, smooth solution to iut=Δu−‖u‖ p−1u. If n=1 and 2p≤3, then there does not exist any finite energy free solution v such that ∥u(t)−v(t)∥2→0 as t→+∞. This extends a theorem of Strauss in which the same result was proved for 1p≤2.
Jacqueline E. Barab (Thu,) studied this question.