On the Complexity of Bifurcation in a Family of Equations Involving Lipschitz Operators
Arno Langenbach · Mathematische Nachrichten · 2002
We investigate branches of eigenfunctions starting from a bifurcation point of Equation (1.2), x — F(x, λ) = 0, in a Banach space X for real λ. Elements of the total derivative of F(·, λ) in zero may create different directions of bifurcating branches depending in a complicated way on neighbouring λ. In special situatons we are able to calculate curves of eigenfunctions leading to segments consisting entirely of bifurcation points λt. In this investigation the finite dimensional Ljapunov-Schmidt branching equations are used, simplified by trunkation.