Existence and stability of solutions for maximal element theorem on Hadamard manifolds with applications

详细信息    查看全文

• 作者：Zhe  ; Yang  ; ;   ; ^a ;   ; ^{zheyang211@163.com} ; Yong Jian  ; Pu^a
• 关键词：Maximal element theorem ; Hadamard manifolds ; Essential set ; Essential component ; Variational relation problems ; Weakly Pareto&ndash ; Nash equilibrium
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：January 2012
• 年：2012
• 卷：75
• 期：2
• 页码：516-525
• 全文大小：249 K

文摘

In this paper, maximal element theorem on Hadamard manifolds is established. First, we prove the existence of solutions for maximal element theorem on Hadamard manifolds. Further, we prove that most of problems in maximal element theorem on Hadamard manifolds (in the sense of Baire category) are essential and that, for any problem in maximal element theorem on Hadamard manifolds, there exists at least one essential component of its solution set. As applications, we study existence and stability of solutions for variational relation problems on Hadamard manifolds, and existence and stability of weakly Pareto¨CNash equilibrium points for -person multi-objective games on Hadamard manifolds.