Bifurcation of critical points along gap-continuous families of subspaces

TL;DR

This paper investigates how critical points of twice differentiable functionals on Hilbert spaces bifurcate along continuously varying subspace families, with applications to semilinear ODE systems.

Contribution

It introduces a framework for analyzing bifurcation of critical points along gap-continuous subspace families and applies it to semilinear differential equations.

Findings

Bifurcation points are characterized along gap-continuous subspace families.

Results provide conditions for the existence of bifurcating branches of critical points.

Applications demonstrate the relevance to semilinear ODE systems.

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.