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Sharp condition of global well-posedness for inhomogeneous nonlinear Schrödinger equation

  • * Corresponding author: Chao Yang

    * Corresponding author: Chao Yang
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  • This paper studies the Cauchy problem of Schrödinger equation with inhomogeneous nonlinear term $ V(x)|\varphi|^{p-1}\varphi $ in $ \mathbb{R}^n $. For the case $ p > 1+\frac{4(1+\varepsilon_0)}{n} (0 < \varepsilon_0 < \frac{2}{n-2}) $, by introducing a potential well, we obtain some invariant sets of solution and give a sharp condition of global existence and finite time blowup of solution; for the case $ p < 1+\frac{4}{n} $, we obtain the global existence of solution for any initial data in $ H^1 (\mathbb{R}^n) $.

    Mathematics Subject Classification: Primary: 35Q55, 35G25.


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