Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory
Dynamical Systems
2021-11-17 v1 Analysis of PDEs
Functional Analysis
Abstract
This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous bifurcation theorems for potential operators by weakening standard assumptions on the differentiability of the involved functionals, which opens up a way of bifurcation studies for quasi-linear elliptic boundary value problems.
Cite
@article{arxiv.2111.08689,
title = {Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory},
author = {Guangcun Lu},
journal= {arXiv preprint arXiv:2111.08689},
year = {2021}
}
Comments
75 pages. Revision and extension for Part I (Abstract bifurcation theory) and Part III (Appendix) in arXiv:1712.03479v2[math.FA]. Discrete Contin. Dyn. Syst., (2021) online. First one of a series of papers about author's bifurcation research program