Multiple critical points of a functional in product spaces with applications to elliptic systems

报告人：程锡友 教授

报告题目：Multiple critical points of a functional in product spaces with applications to elliptic systems

报告时间：2026年10月31日（周六）下午3:00-5:00

报告地点：云龙校区6号楼417室

主办单位：数学与统计学院、数学研究院、科学技术研究院

报告人简介：

程锡友，兰州大学数学与统计学院教授，主要从事非线性泛函分析、非线性椭圆型方程的研究，在J. Geom. Anal.、JDE、Sci. China Math.、DCDS、Proc. Roy. Soc. Edinburgh Sect. A等杂志上发表论文30余篇。

报告摘要：

In this paper, we deal with the existence and multiplicity of component-wise nontrivial critical points (i.e., whose components are both nonzero) for an abstract C^1-functional J defined in X × X with X being a reflexive Banach space. Applying the Nehari manifold method and the minimization method along with the geometric properties of the constructed functions, we investigate the existence and multiplicity of component-wise nontrivial critical points of J . As applications, we prove the existence and multiplicity of component-wise nontrivial solutions for the second-order and fourth-order elliptic systems. Our theoretical results improve and extend the relevant results in the existing literature.