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| 摘要: |
| 本文研究了Banach空间中一类新的微分混合均衡问题（简记为（DME））.利用Fan-KKM定理和Ky Fan极大极小不等式，分别证明了在某些合适条件下混合均衡问题解的存在性.此外，证明了一类集值映射的叠加可测性和上半连续性.最后，利用半群理论和Filippov隐函数引理，获得了关于（DME）问题温和解的存在性定理并讨论了解集合的紧性.所得结果丰富并扩展了均衡理论. |
| 关键词: 微分混合均衡问题 Banach空间 Fan-KKM定理 Ky Fan极大极小不等式 Filippov隐函数引理 |
| DOI： |
| 分类号:O177.91 |
| 基金项目:Supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province(KYCX20 1321). |
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| DIFFERENTIAL MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACE |
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WANG Zhi-wei,JU Gui-yin
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| Abstract: |
| In this paper, we investigate a new class of differential mixed equilibrium problems ((DME), for short) in Banach space. By using Fan-KKM theorem and Ky Fan's minmax inequality, we respectively prove the existence of solutions for mixed equilibrium problems under some suitable conditions. Moreover, we prove the superpositional measurability and upper semicontinuity for a class of set-valued mappings. Finally, by using the theory of semigroups and Filippov implicit function lemma, we obtain the existence theorem concerned with the mild solutions for (DME) and discuss the compactness of the solution set. The results enrich and extend the theory of equilibrium. |
| Key words: differential mixed equilibrium problems Banach space Fan-KKM theorem Ky Fan's minmax inequality Filippov implicit function lemma |
