Scaling solution branches of one-parameter bifurcation problems
The authors study an abstract one-parameter bifurcation problem and, in order to investigate the steady state and the Hopf bifurcations, they apply the Lyapunov-Schmidt reduction method for obtaining an equivalent lower dimensional system of algebraic equations. They use the Böhmer-Mei method for exploiting the scales of solution branches and unify the two succesive steps in the standard Lyapunov-Schmidt method. It is also defined an algorithm for analyzing the bifurcation structure and for the branch switching in solution branches of the considered problem. As an application, there are studied bifurcations of a semilinear elliptic problem on square or hexagonal domains. There are also found numerical values of the coefficients in the reduced bifurcation equations on these domains.
semilinear elliptic problem on square or heagonal domains
scientific article; zbMATH DE number 1005487