Morse theory methods for quasi-linear elliptic systems of higher order

2017/02/22 by Guangcun Lu, Lu, Guangcun
Computer Science · Mathematics · #49J45 (Primary) #49J52 #58E05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.06667

openalex publication_date 2017/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type result. With them some critical point theorems and famous bifurcation theorems are generalized. Then we show that these are applicable to studies of quasi-linear elliptic equations and systems of higher order given by multi-dimensional variational problems as in (1.3).

Related

• Morse theory methods for a class of quasi-linear elliptic systems of higher order
• The splitting lemmas for nonsmooth functionals on Hilbert spaces
• Parameterized splitting theorems and bifurcations for potential operators
• Morse homology for a class of elliptic partial differential equations
• Algebraic Morse theory and homological perturbation theory