| Volume 7, Number 1, 2017, Pages 249-263 DOI：10.11948/2017017 |
| Divergent Solution to the Nonlinear Schr\"{o}dinger Equation with the Combined Power-Type Nonlinearities |
| Jing Li,Boling Guo |
| Keywords:Nonlinear Schr\"{o}dinger equation, combined power-type nonlinearities, blow-up. |
| Abstract: |
| In this paper, we consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation with combined power-type nonlinearities, which is mass-critical/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 $H^1$-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time. |
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