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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第六十二)

发布者:鲍旭东   发布时间:2021-11-01  浏览次数:304

2021非线性分析与偏微分方程学术报告

报告题目1:Maximum principles and monotonicity of solutions for fractional p-equations in unbounded domains

报告人刘招江西科技师范大学

报告时间:114日(周四),14:00-15:00

腾讯会议ID:  275 998 965



摘要  In this talk, we consider the non-linear equations in unbounded domains involving the fractional p-Laplacian. We establish a maximum principle in unbounded domains by estimating the singular integral along a sequence of approximate maximum points. Then, we obtain the asymptotic behavior of solutions far away from the boundary as well as the monotonicity and uniqueness of solutions. Our results are extensions of the classical Laplacian by Berestycki, Caffarelli and Nirenberg and the fractional Laplacian by Dipierro, Soave and Valdinoci.

 

报告人简介刘招,江西科技师范大学副教授,主要研究领域为非线性偏微分方程及其应用,主要研究结果发表在JDE、CVPDESIAM J.Math. Anal. Trans.Amer. Math.Soc.等国际学术期刊上

 

报告题目2:  On minima of sum of theta functions and application to Mueller-Ho Conjecture

报告人: 罗森平江西师范大学

报告时间:114日(周四),15:00-16:00

腾讯会议ID:  275 998 965


摘要 We found and proved a novel and complete result on the minimizer problem for theta functions with parameter rho.  As a consequence, we gave a partial and positive answer to optimal lattice arrangements of vortices in competing systems of Bose-Einstein condensates as conjectured (and numerically and experimentally verified) by Mueller-Ho 《PRL》2002, this is the first progress on Mueller-Ho conjecture.

 

报告人简介罗森平,江西师范大学副教授,博士毕业于清华大学,主要研究领域为非线性偏微分方程及其应用,担任国家青年基金项目主持人;主要研究结果发表在Proc. Amer. Math. Nonlinearty. SIAM J. Math. Anal. 等国际学术期刊上


报告题目3Existence and multiplicity of sign-changing solutions for quasilinear Schrodinger equations with sub-cubic nonlinearity

报告人张建军重庆交通大学)

会议时间:114日(周四),16:00-17:00

腾讯会议ID:  275 998 965


摘要 In this paper, we consider the quasilinear Schrodinger equation


where V and g are continuous functions. Without the coercive condition on V or the monotonicity condition on g, we show that the problem above has a least energy sign-changing solution and infinitely many sign-changing solutions. Our results especially solve the problem above in the case where  and complete some recent related works on sign-changing solutions, in the sense that, in the literature only the case  was considered. The main results in the present paper are obtained by a new perturbation approach and the method of invariant sets of descending flow. In addition, in some cases where the functional merely satisfies the Cerami condition, a deformation lemma under the Cerami condition is developed. This talk is based on joint work with Hui Zhang, Zhisu Liu and Chun-Lei Tang.

 

报告人简介: 张建军,重庆交通大学教授、清华大学博士,Mathematics Review评论员,2012年-2014年南开大学陈省身数学研究所博士后,2014年-2015年巴西帕拉伊巴联邦大学博士后,2015年-2016年和2018年-2019年意大利因苏布里亚大学博士后,2018年7月获得意大利副教授国家资格认证,主持国家自然科学基金-面上项目、国际(地区)合作交流项目、意大利伦巴第研究员基金(Global ERC)和中国博士后基金(二等)各一项,先后应邀访问美国,德国,意大利,葡萄牙,西班牙和巴西等多所研究机构,并多次在国际会议上作学术报告。研究领域主要包括非线分析中的变分与拓扑方法,非线性椭圆方程等,迄今已在包括Communications in Partial Differential Equations,Journal of Differential Equations, Calculus of Variations and Partial Differential Equations, Nonlinearity, Proceedings of the Royal Society of Edinburgh, Section A Mathematics,Journal of the London Mathematical Society, Annali di Matematica Pura ed Applicata, Communications in Contemporary Mathematics等刊物上发表SCI论文40余篇,其中ESI高被引4篇。

 

邀请人:非线性分析与PDE团队