Abstract
In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equation with combined power-type nonlinearities, which is masscritical/supercr-itical, and energy-subcritical. Combing Du, Wu and Zhang' argument with the variational method, we prove that if the energy of the initial data is negative (or under some more general condition), then the <i>H</i><sup>1</sup>-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time.
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