Nonlinear homogeneous perturbation of the discrete spectrum of a self-adjoint operator and a new Constrained Saddle Point Theorem

We prove a Critical Point Theorem for C1 functionals on the unit sphere of a separable Hilbert space H which improves a previous result of ours. This is applied in nonlinear eigenvalue theory to study the effect of suitably restricted homogeneous perturbations upon the discrete spectrum of a bounded self-adjoint operator in H.