  Using theoretical arguments, we prove the numerically well-known fact that
the eigenvalues of all localized stationary solutions of the cubic-quintic 2D+1
nonlinear Schrodinger equation exhibit an upper cut-off value. The existence of
the cut-off is inferred using Gagliardo-Nirenberg and Holder inequalities
together with Pohozaev identities. We also show that, in the limit of
eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear
Schrodinger equation behave similarly to those of the cubic nonlinear
Schrodinger equation.
