EXISTENCE RESULTS FOR VECTOR SADDLE POINTS PROBLEMS

Abstract

In this paper, we study the existence of solutions for vector saddle points problems in a general setting. Our approach, first, is based on the KKM lemma and a relaxation of the $C-$ lower semicontinuity notion introduced by T.Tanaka by means of an extension to the vector setting of a Brézis-Nirenberg-Stampacchia condition, and arguments from generalized convexity. This leads us to generalize and improve some new existence results on vector saddle points problems. In the second approach, we establish an existence result for vector saddle point problems under a paracompacity assumption.