Solution Branches for Non-linear Equilibrium Problems--Bifurcation and Domain Perturbations

Consider the following simple, but typical, example of a non-linearequilibrium (differential equation) problem: u = –f(u) for (x, y) D, u = 0 for (x, y) D. Usually the eigenvalues of the (small u) linearized problemare simple, and each simple eigen value generates two solutionbranches for the full problem. However, the full problem nearlyalways has many other solution branches, and this paper describeshow to find these other branches and why they arise.