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数学学科现代分析及其应用研究所(2021非线性分析与偏微分方程系列报告会四十九)

发布者:戴 情   发布时间:2021-07-16  浏览次数:130

报告题目High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents

报告人高发顺河南城建学院

报告时间:717日(周六),8:30-9:30

报告地点:21幢-427

 

摘要 We are interested in the critical coupled Hartree system

$$

\left\{\begin{array}{ll}

-\Delta u+ V_1(x)u

=\alpha_1\big(|x|^{-4}\ast u^{2}\big)u+\beta \big(|x|^{-4}\ast v^{2}\big)u

&\mbox{in}\ \R^N,\\[1mm]

-\Delta v+ V_2(x)v

=\alpha_2\big(|x|^{-4}\ast v^{2}\big)v +\beta\big(|x|^{-4}\ast u^{2}\big)v

&\mbox{in}\ \R^N,

\end{array}\right.

$$

where $N\geq5$,

$\beta>\max\{\alpha_1,\alpha_2\}\geq\min\{\alpha_1,\alpha_2\}>0$,

and $V_1,\,V_2\in L^{N/2}(\R^N)\cap L_{\text{loc}}^{\infty}(\R^N)$ are

nonnegative potential functions. By applying moving sphere arguments in integral form, we are able to classify the positive solutions of the critical Hartree system with $V_1=V_2=0$ and prove

the uniqueness of positive solutions up to translation and dilation, which is of interest independently. By assuming $|V_1|_{L^{N/2}(\R^N)}+|V_2|_{L^{N/2}(\R^N)}>0$ suitably small and using the uniqueness property, we will establish a nonlocal version of global compactness lemma to obtain the existence of positive solutions of high energy for the critical Hartree system variationally.

 

报告人简介高发顺河南城建学院副教授。20186月博士毕业于浙江师范大学2019年博士学位论文获得了浙江省优秀博士学位论文。主要从事非线性分析和临界点理论与变分学的研究。研究成果主要发表J. Differential Equations》、《Sci China Math》、《Nonlinearity》Proc. Roy. Soc. Edinburgh Sect. A》、《Nonlinear Anal.》、《Commun. Contemp. Math.》、《Discret. Cont. Dyn. Sys.-A》、《Z. Angew. Math. Phys.》等国际知名学术期刊上2020年主持国家自然科学基金青年项目。

 

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