International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 429-438

Critical point theorems

H. Boukhrisse and M. Moussaoui

Department of Mathematics, Faculty of Sciences, University Mohammed I, Oujda, Morocco

Received 12 December 2000

Copyright © 2002 H. Boukhrisse and M. Moussaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let H be a Hilbert space such that H=VW, 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 is of class 𝒞2 and 𝒞1, respectively.