We use Conley index theory to solve the singular boundary value problem Duxx+ f(u, ux, x) = 0 on an interval [−1, 1], where u ∈ R n and D is a diagonal matrix, with separated boundary conditions. Since we use topological methods the assumptions we need are weaker then the standard set of assumptions. The Conley index theory is used here not for detection of an invariant set, but for tracking ce...
