题目： Solving Singularly Perturbed Neumann Problems for Multiple Solutions

报告人： 谢资清 教授

（湖南师范大学数学与计算机科学学院院长）

Abstract : 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.

时间：2019年7月2日（周二)

上午10:30-11:30

地点：565net必赢客户端本部教二楼627教室

联系人：赵旭鹰

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