International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 7, Pages 429-438
Critical point theorems
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 be a Hilbert space such that , where
and are two closed subspaces of . We generalize an abstract theorem due to Lazer et al. (1975) and a theorem given by Moussaoui (1990-1991) to the case where and
are not necessarily finite dimensional. We give two mini-max theorems where the functional is of class and , respectively.