Discriminant sets and layerings of bifurcating solutions of Fredholm equations (Q2487421)

The authors present a review of their results on the generalized Cacciopoli scheme leading to a nonlocal Lyapounov-Schmidt method for nonlinear Fredholm mappigs both with parameter and without it with applications to stationary and dynamic (Poincaré-Andronov-Hopf) bifurcation problems and also under symmetry conditions. These results are especially effective in the variational case. On this base elegant applications to a classification of postcritical stationary phases of cristalline ferroelectrics and bifurcations of periodic waves in elastic and crystalline media are investigated.