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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）

 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：7月17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 $V_1,\,V_2\in L^{N/2}(\R^N)\cap L_{\text{loc}}^{\infty}(\R^N)$ arenonnegative 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 provethe 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。2018年6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。研究成果主要发表于《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。 邀请人：非线性分析与PDE团队