报告题目1：A Stage-structured predator-prey model with predation on juvenile and adult prey

报告人：    刘守宗  博士

报告时间：2018年10月23日（周二）16:30—17:00

报告地点：威廉希尔学术报告厅

报告摘要： In this talk, a stage-structured predator-prey model of Holling type II functional response is formulated to investigate the impact of predation over both juvenile and adult prey by the juvenile predator. It is shown that the threshold dynamics can be determined by the net reproductive number of the predator population R₀. The predator-free equilibrium is globally stable if R₀<1 , while the predator persists if R₀>1. Numerical simulations are also carried out to illustrate our theoretical results.

报告题目2：The existence and nonexistence of solutions for quasilinear Schrodinger equation

报告人：    薛艳昉  博士

报告时间：2018年10月23日（周二）17:00—17:30 

报告地点：威廉希尔学术报告厅

报告摘要：This talk is concerned with the existence and nonexistence of standing wave solutions for quasilinear Schrodinger equation with various potential. The approaches we used are the variational method, the critical point theory and analytical techniques.  Firstly, we are concerned with the  quasilinear Schrodinger equation with asymptotically periodic potential. By using a change of variables, the quasilinear problem is transformed into a semilinear one. Then we use a Nehari-type constraint to get the existence result. Secondly, we investigate the  quasilinear Schrodinger  problem under a general nonlinear term. We obtain a positive solution by the monotonicity trick and the mountain pass lemma. Moreover, we prove a nonexistence result by employing the Pohozaev manifold. Finally, we establish the existence of bound state solutions. The proofs are based on the Pohozaev manifold and a linking theorem.

刘守宗，博士，2018年获美国 Southern Illinois University at Carbondale 博士学位，主要从事生物数学领域的研究，在国内外重要学术期刊 Nonlinear Dynamics, Journal of Biological Dynamics 等发表学术论文7篇。

薛艳昉，博士，2018年于西南大学获理学博士学位，主要从事非线性泛函分析的研究。在国内外重要学术期刊 Advances in Nonlinear Analysis, Commun. Pure Appl. Anal., Comput. Math. Appl.,  Annales Polonici Mathematici 等发表学术论文4篇。

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                                                                                        威廉希尔

                                                                                       2018年10月18日