Remarks on the preservation and breaking of translational symmetry for a class of ODEs

Remarks on the preservation and breaking of translational symmetry for a class of ODEs

In this paper, we provide both a preservation and breaking of symmetry theorem for 2π-periodic problems of the form −u′′(t)+g(u(t))=f(t)u(0)−u(2π)=u′(0)−u′(2π)=0where g:R→Ris a given C1function and f:[0,2π]→Ris continuous. We provide a preservation of symmetry result that is analogous to one given b...

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Bibliografiska uppgifter
Huvudupphovsmän: Edward Huynh, Keoni Castellano
Materialtyp: Artikel
Språk:English
Publicerad: Elsevier 2022-11-01
Serie:Examples and Counterexamples
Ämnen:
Periodic solutions
Symmetry breaking
Symmetry preservation
Group action
Critical groups
Morse index
Länkar:http://www.sciencedirect.com/science/article/pii/S2666657X22000167

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