SCALING SOLUTION BRANCHES OF ONE-PARAMETER BIFURCATION PROBLEMS

We consider an algorithm for analyzing bifurcation structure and for b ranch switching in solution branches of one-parameter dependent proble ms. Based on Liapunov-Schmidt methods and analyses of scales of soluti ons, we verify the existence of bifurcating solution branches successi vely via truncated Taylor expansions of the reduced bifurcation equati ons and an enlarged system. As examples, bifurcations of semilinear el liptic differential equations are studied on square and hexagon domain s. (C) 1996 Academic Press, Inc.