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Instability of standing waves for a class of nonlinear Schrödinger equations |
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| Authors: | Ji Shu Jian Zhang |
| Institution: | a Sichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University, Chengdu 610066, China b College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China c College of Mathematics, Sichuan University, Chengdu 610064, China |
| Abstract: | This paper discusses a class of nonlinear Schrödinger equations with different power nonlinearities. We first establish the existence of standing wave associated with the ground states by variational calculus. Then by the potential well argument and the concavity method, we get a sharp condition for blowup and global existence to the solutions of the Cauchy problem and answer such a problem: how small are the initial data, the global solutions exist? At last we prove the instability of standing wave by combing those results. |
| Keywords: | Nonlinear Schrö dinger equations Ground state Standing wave Blowup Global existence |
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