A generalized mountain-pass theorem: the existence of multiple critical points

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to u parallel to = rho >= alpha > J(0) and that here exits a point b is an element of H with parallel to b parallel to > rho and with J(b)