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学术报告

标题：The mountain pass theorem in terms of tangencies

报告时间：2024年05月10日（星期五）14:30-15:30

报告地点：惟真楼309

主讲人：Tien-Son Pham（越南大叻大学，教授）

主办单位：前沿交叉研究院

报告内容简介：

This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely,  let be a locally Lipschitz function with a mountain pass geometry. Let

where A is the set of all continuous paths joining two points in Rⁿ . We show that either c is a critical value of f or c is a tangency value at infinity of .This reduces to the Mountain Pass Theorem of Ambrosetti and Rabinowitz in the case where the function is definable (e.g., semi-algebraic) in an o-minimal structure.