New Quantitative Deformation Lemma and New Mountain Pass Theorem

2014/02/19 by Liang Ding, Ding, Liang, Fode Zhang +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1402.4602

openalex publication_date 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain a new quantitative deformation Lemma so that we can obtain more critical points, especially for supinf critical value c₁, x=φ^-1(c₁) is a new critical point. For infmax critical value c₂, we can obtain two new critical points x = 0 (valley point) and x = e(peak point) ,comparing with Willem's variant of the mountain pass theorem of Ambrosetti-Rabinowitz,in which φ(e)≤φ(0)

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