On the Complexity of Bifurcation in a Family of Equations Involving Lipschitz Operators

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 λ_t. In this investigation the finite dimensional Ljapunov‐Schmidt branching equations are used, simplified by trunkation.