Existence Results for Vector Saddle Point Problems in the n-direction

Kanokwan Sitthithakerngkiet

Abstract

In this paper, we introduce the n-vectorial saddle point problem (for short $VSP_n$) which defined on n-dimensional saddle point where (n $>$ 2) by focusing only on the saddle point of order one. For that matter, we prove existence saddle point of $(VSP_n)$ under assuming compactness and uncompactness by using Fan-KKM Theorem. This result improves and extends some literatures on the existence theorems of saddle point problems.