Global bifurcation for a class of nonlinear ODEs
arXiv:2107.08181 · doi:10.1007/s40863-022-00290-3
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.
LaTeX2e, 19 pages, 2 figures, final (revised) version. To appear in São Paulo J. Math. Sci