BIFURCATION AND HOPF BIFURCATION AT MULTIPLE EIGENVALUES FOR EQUATIONS WITH LIPSCHITZ MAPPINGS

摘要

Some results on the existence of bifurcation and Hopf bifurcation at multiple eigenvalues for abstract equations concerning Lipschitz continuous mappings in Banach spaces are proved. The obtained results improve some well-known bifurcation results by Crandall and Rabinowitz, McLeod and Sattinger, Hopf etc. in the case involving Lipschitz continuous mappings. Some illustrative examples are given.