Global bifurcation for a class of nonlinear ODEs
Differential Geometry
2022-07-25 v2 Classical Analysis and ODEs
Abstract
We briefly survey global bifurcation techniques, and illustrate their use by finding multiple positive periodic solutions to a class of second order quasilinear ODEs related to the Yamabe problem. As an application, we give a bifurcation-theoretic proof of a classical nonuniqueness result for conformal metrics with constant scalar curvature, that was independently discovered by O. Kobayashi and R. Schoen in the 1980s.
Keywords
Cite
@article{arxiv.2107.08181,
title = {Global bifurcation for a class of nonlinear ODEs},
author = {Renato G. Bettiol and Paolo Piccione},
journal= {arXiv preprint arXiv:2107.08181},
year = {2022}
}
Comments
LaTeX2e, 19 pages, 2 figures, final (revised) version. To appear in S\~ao Paulo J. Math. Sci