A VARIATIONAL APPROACH TO MULTIPLE LAYERS OF THE BISTABLE EQUATION INLONG TUBES

Multiple-layer solutions of the balanced bistable equation in infinite tubes are constructed via a variational method. I start with a charac terization of Palais-Smale sequences which easily gives some global mi nima in the desired function classes as single layers. Assuming these minima are isolated as critical points, I paste them together to serve as an approximate multiple-layer solution. If there were no exact sol utions near the approximate one, the negative gradient flow of the ene rgy functional would significantly lower the energy. On the other hand , if the minima are kept far from each other, the energy of a function near the approximate solution is not much less than that of the appro ximate solution. This contradiction proves the existence of a solution .