Hopf bifurcation at multiple eigenvalues with zero eigenvalue

Abstract

SynopsisWe give local results related to Hopf bifurcation for parabolic equations. The linear part about the equilibrium point can have zero eigenvalues. In our results the information about the perturbation is essential and it is possible to obtain bifurcation even if some ‘i’ or zero remains on the imaginary axis for all values of the parameter.