Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

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.

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

References in corpus (3)

• Symmetric Liapunov center theorem
• Equivariant bifurcation in geometric variational problems
• Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems

Cited by in corpus (2)

• Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems
• A note on bifurcation theorems of Rabinowitz type