In this talk, we shall exhibit a mini-max characterization of the second eigenvalue of the p-Laplacian operator on p-quasi-open sets, using a construction based on minimizing movements on non-linear gradient flows. The following outline shall be presented: the notion of non-linear eigenvalues and their properties, the statement of the characterization, the notion of Quasi-open sets, and a sketch of the proof of the theorem. This is based on a joint work with Nicola Fusco and Yi Zhang.