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

Eigenvalue cut-off in the cubic-quintic nonlinear Schrodinger equation