A Note on Breaking of Symmetry for a Class of Variational Problems
Document Type
Article
Publication Date
7-2-2019
Publication Title
Applied Mathematics Letters
Volume
98
First page number:
329
Last page number:
335
Abstract
In this note we present a symmetry breaking result for a class of 2π− periodic problems of the form: −u′′(t)=g(u(t))+f(t); u(0)−u(2π)=u′(0)−u′(2π)=0 where g:R→R is a given C1 function and f:[0,2π]→R is continuous. Our approach is inspired on Willem’s paper (Willem, 1989) and uses actions of finite groups which are not usually considered in the literature.
Keywords
Periodic solutions; Symmetry breaking; Group action; Critical groups; Morse index
Disciplines
Mathematics
Language
English
Repository Citation
Costa, D. G.,
Fang, Z.
(2019).
A Note on Breaking of Symmetry for a Class of Variational Problems.
Applied Mathematics Letters, 98
329-335.
http://dx.doi.org/10.1016/j.aml.2019.06.031