Bifurcation and symmetry in problems of capillary-gravity waves.
Bifurcation of free vibrations for completely resonant wave equations
We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent.
Bifurcation results for a class of perturbed Fredholm maps.