Bifurcation of critical points along gap-continuous families of subspaces

Abstract

We consider the restriction of twice differentiable functionals on a Hilbert space to families of subspaces that vary continuously with respect to the gap metric. We study bifurcation of branches of critical points along these families, and apply our results to semilinear systems of ordinary differential equations.

arXiv commentv2: 15 pages, minor revisions and improved example in Section 5