Speaker: Zongming Guo, doctoral supervisor, College of Mathematics and Information Science, Henan Normal University

Date: May 9, 2024

Time: 10:45-11:30

Location: B1032, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Positive singular solutions with an isolated singular point for boundary valueproblems of some second and fourth order elliptic equations are constructed. Asymptotic expansions up to arbitrary orders at the singular point for prescribed solutions of the equations are established firstly. Then, introducing the appropriate weighted H\"older spaces according to the established asymptotic expansions and the related operators of the equations, we construct super-solutions for the boundary value problems via fixed point arguments. The variational solutions of the boundary value problems are reconstructed as sub-solutions. Infinitely many positive singular solutions are constructed via sub- and super-solution arguments.

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https://www.view.sdu.edu.cn/info/1020/190639.htm