在线阅读 --自然科学版 2018年3期《具有混合非线性项的Schrödinger方程临界值的存在性》
具有混合非线性项的Schrödinger方程临界值的存在性--[在线阅读]
尤念念
河海大学 理学院, 江苏 南京 211100
起止页码: 190--197页
DOI: 10.13763/j.cnki.jhebnu.nse.2018.03.002
摘要
通过将约束变分问题中的泛函转化为非负泛函,利用Schwartz对称化、Lagrange乘子及最优Sobolev不等式等经典变分方法,研究了混合非线性项为质量超临界项加上能量临界或者次临界聚焦项的Schrödinger方程临界值的存在性问题,证明了临界值的存在性,并给出了临界值,为进一步研究此类方程的整体适定性和散射奠定了基础.

Existence of the Threshold for Some Combined Nonlinear Schrödinger Equation
YOU Niannian
College of Science, Hohai University, Jiangsu Nanjing 211100, China
Abstract:
We mainly study the existence of the threshold for the Schrödinger equation with combined nonlinearities,one of which is mass-supercritical and the other is focusing energy-criticalor energy-subcritical by means of transforming the functional in the constrained variational problem to a non-negative functional.Moreover,by using the classical variational methods such as Schwartz symmetrization,Lagrange multiplier and the optimal Sobolev inequality,we obtain the threshold and proved the existence of the threshold.It lays a foundation for the further study about the global well-posedness and scattering of such equation.

收稿日期: 2017-09-12
基金项目: 国家自然科学基金(11526072,51509073)

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