Critical point theorems

Abstract

Let H be a Hilbert space such that H=V⊕W, where V and W are two closed subspaces of H. We generalize an abstract theorem due to Lazer et al. (1975) and a theorem given by Moussaoui (1990-1991) to the case where V and W are not necessarily finite dimensional. We give two mini-max theorems where the functional Φ:H→ℝ is of class 𝒞2 and 𝒞1, respectively.