A Note on Breaking of Symmetry for a Class of Variational Problems
Applied Mathematics Letters
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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.
Periodic solutions; Symmetry breaking; Group action; Critical groups; Morse index
Costa, D. G.,
A Note on Breaking of Symmetry for a Class of Variational Problems.
Applied Mathematics Letters, 98