学术报告(谢资清 8.18)

发布人:周妍 发布日期:2018-07-27
活动时间
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学术报告(谢资清 8.18

 

题目:Solving Singularly Perturbed Neumann Problems for Multiple Solutions

主讲人:谢资清 教授(湖南师范大学数学与统计学院

时间:2018818日上午100011:30

地点:新数学楼415

 

摘要:

In this talk, based on the analysis of  bifurcation points and Morse indices of trivial solutions at any perturbation value, the generating process of nontrivial positive solutions for a general singularly perturbed Neumann boundary value problem is developed. The bifurcation points of each trivial solution and then the exact critical perturbation value $\varepsilon_c$ which determines the existence or non-existence of nontrivial positive solutions are verified. An efficient local minimax method based on the bifurcation and Morse theory is proposed to compute both M-type and W-type saddle points by introducing an adaptive local refinement strategy, a continuation strategy for initial selection and the Newton method to improve the convergence speed.  Extensive numerical results are reported to investigate the critical value $\varepsilon_c$ and present interesting properties of different types of multiple solutions.

 

数学学院

2018727