We study the ground state problem of the nonlinear Schrodinger functional with a mass-critical inhomogeneous nonlinear term. We provide the optimal condition for the existence of ground states and show that in the critical focusing regime there is a universal blow-up profile given by the unique optimizer of a Gagliardo-Nirenberg interpolation inequality.

中文翻译：

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质量临界非齐次非线性薛定谔泛函的基态

我们研究了具有质量临界非齐次非线性项的非线性薛定谔泛函的基态问题。我们为基态的存在提供了最佳条件，并表明在临界聚焦状态下，存在由 Gagliardo-Nirenberg 插值不等式的独特优化器给出的通用爆炸曲线。