不具单调性的均衡系统问题的解的存在性

Existence of Solutions to Systems of Equilibrium Problems Without Monotonicity

该文引入并研究了一类不具单调性的均衡系统问题.利用Brouwer不定点定理,在有限维空间下得到了均衡系统问题的解的存在性.在无限维情形,通过引入函数族的(S)+-条件,证明了基于(S)+-条件下的均衡系统问题的解的存在性.

In this paper, the authors introduce and study systems of equilibrium problems without monotonicity. By using Brouwer fixed point theorem, the authors obtain an existence theorem in the setting of finite dimensional spaces. In the case of infinite dimensional spaces, the authors introduce the definition of （S）＋ condition for a family of functions and prove the existence of solutions to systems of equilibrium problems based on （S）＋ conditions.