BRANCH SWITCHING AT A CORANK-4 BIFURCATION POINT OF SEMILINEAR ELLIPTIC PROBLEMS WITH SYMMETRY

Branch switching of the problem [GRAPHICS] at a corank-4 bifurcation p oint is investigated by exploiting symmetry and other properties of th e operator. Here f:R --> R is a smooth odd function. The singularity o f the corank-4 bifurcation point is decomposed into various subspaces via symmetries such that all solution branches can be followed by cont inuation methods and their modifications. At the same time, a modified Lyapunov-Schmidt method is used to determine solution branches having little symmetry on a slightly enlarged system in appropriate subspace s. We find altogether 40 different solution branches. Among them we ha ve 13 solutions, such that none of these solutions can be generated by conjugation or hidden symmetries from any other solutions.