International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 521-528
doi:10.1155/S0161171296000725
On minimax theory in two Hilbert spaces
E.M. El-Kholy1
and Hanan Ali Abdou2
1Faculty of Science, Department of Mathematics, Tanta University, Tanta, Egypt
2Faculty of Education, Department of Mathematics, Ain Shams University, Cairo, Egypt
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.