In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equation with combined power-type nonlinearities, which is masscritical/supercritical, 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 H1-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time. ©...
