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- W4286976646 abstract "In this paper, we provide both a preservation and breaking of symmetry theorem for $2pi$-periodic problems of the form begin{align*} begin{cases} -u''(t) + g(u(t)) = f(t)cr u(0) - u(2pi) = u'(0) - u'(2pi) = 0 end{cases} end{align*} where $g: mathbb{R} to mathbb{R}$ is a given $C^1$ function and $f: [0,2pi] to mathbb{R}$ is continuous. We provide a preservation of symmetry result that is analogous to one given by Willem (Willem, 1989) and a generalization of the theorem given by Costa-Fang (Costa and Fang, 2019). Both of these theorems use group actions that are not normally considered in the literature." @default.
- W4286976646 created "2022-07-25" @default.
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- W4286976646 date "2021-09-14" @default.
- W4286976646 modified "2023-09-27" @default.
- W4286976646 title "Remarks on the preservation and breaking of translational symmetry for a class of ODEs" @default.
- W4286976646 doi "https://doi.org/10.48550/arxiv.2109.06994" @default.
- W4286976646 hasPublicationYear "2021" @default.
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