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A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma
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作者 Cassie Lu 《数学计算(中英文版)》 2023年第2期1-6,共6页
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo... This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question. 展开更多
关键词 brouwer’s Fixed Point Theorem sperner’s Lemma PROOF
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Existence of Solutions to a Generalized System
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作者 Yali Zhao Lin Xing Jia Tao 《Applied Mathematics》 2012年第6期511-516,共6页
In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Furth... In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results. 展开更多
关键词 GENERALIZED system C-strong PsEUDOMONOTONICITY brouwer’s Fixed POINT THEOREM Hemicontinuous MAPPING
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PERIODIC SOLUTIONS OF THE JOSEPHSON EQUATION
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作者 郑作环 《Systems Science and Mathematical Sciences》 SCIE EI CSCD 1990年第2期143-150,共8页
In this paper,the Josephson equation and its autonomous case are considered.It isshown that for |α|【1 and β】γ】1 or β【γ【-1,there is no periodic solution of the autonomousJosephson equation,For the nonautonomo... In this paper,the Josephson equation and its autonomous case are considered.It isshown that for |α|【1 and β】γ】1 or β【γ【-1,there is no periodic solution of the autonomousJosephson equation,For the nonautonomous case,some suffcient conditions for the existence ofperiodic solutions are given. 展开更多
关键词 JOsEPHsON EQUATION periodic solutions brouwer’s theorem sADDLE point stable NODE or FOCUs unstable NODE or FOCUs
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