International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 429-438
doi:10.1155/S0161171202011249
Critical point theorems
H. Boukhrisse
and M. Moussaoui
Department of Mathematics, Faculty of Sciences, University Mohammed I, Oujda, Morocco
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.