International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 521-528
doi:10.1155/S0161171296000725
On manimax theory in two Hilbert spaces
1Faculty of Science, Department of Mathematics, Tanta University, Tanta, Egypt
2Faculty of Education, Department of Mathematics, Ain Shams University, Cairo, Egypt
Received 1 February 1994; Revised 19 April 1995
Copyright © 1996 E. M. El-Kholy and Hanan Ali Abdou. 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.
Abstract
In this paper, we investigated the minimax of the bifunction
J:H1(Ω)xV2→RmxRn, such that
J(v1,v2)=((12a(v1,v1)−L(v1)),v2) where
a(.,.) is a finite symmetric bilinear bicontinuous, coercive form on H1(Ω) and L belongs to the
dual of H1(Ω).
In order to obtain the minimax point we use lagrangian functional.