A variational method for functionals depending on eigenvalues

Abstract We perform a systematic variational method for functionals depending on eigenvalues of Riemannian manifolds. It is based on a new concept of Palais–Smale (PS) sequences that can be constructed thanks to a generalization of classical min‐max methods on functionals to locally Lipschitz functionals. We prove convergence results on these PS sequences emerging from combinations of Laplace eigenvalues or combinations of Steklov eigenvalues in dimension 2.