Parameterized splitting theorems and bifurcations for potential operators

2017/12/10 by Guangcun Lu, Lu, Guangcun
Computer Science · Engineering · Mathematics · #49J45 #49J52 #58E05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1712.03479

openalex publication_date 2017/12/10 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

We show that parameterized versions of splitting theorems in Morse theory can be effectively used to generalize some famous bifurcation theorems for potential operators. In particular, such generalizations based on the author's recent splitting theorems [38, 39, 42, 43] and that of [8] are given though potential operators in [42, 43] have weaker differentiability, even discontinuous. As applications, we obtain many bifurcation results for quasi-linear elliptic Euler equations and systems of higher order.

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