Homology of saddle point reduction and applications to resonant elliptic systems

2012/08/27 by Chong Li, Li, Chong, Shibo Liu +1
Computer Science · Mathematics · #35J60 #58E05 #Advanced Mathematical Modeling in Engineering #Algebraic Topology (math.AT) #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #math.AT #msc:35J60 #msc:58E05

paper · pdf · doi:10.48550/arxiv.1208.5312

15 pages, 1 figures

arxiv created 2012/08/27 · openalex publication_date 2012/08/27 · arxiv updated 2012/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the setting of saddle point reduction, we prove that the critical groups of the original functional and the reduced functional are isomorphic. As application, we obtain two nontrivial solutions for elliptic gradient systems which may be resonant both at the origin and at infinity. The difficulty that the variational functional does not satisfy the Palais-Smale condition is overcame by taking advantage of saddle point reduction. Our abstract results on critical groups are crucial.

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