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研究生:劉恩豪
研究生(外文):EN-HAO LIU
論文名稱:無強制條件的擬變分不等式
論文名稱(外文):Noncoercive Quasi-variational Inequalities
指導教授:朱亮儒朱亮儒引用關係
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:17
中文關鍵詞:無強制性擬變分不等式擬變分不等式擬凸函數極大極小不等式凹退函數凹退錐
外文關鍵詞:Noncoercive quasi-variational inequalityquasi-variational inequalityquasi-convex functionrecession functionrecession coneminimax inequality
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變分不等式的理論是研究一制化與一般化格式的非線性問題之有效工具.在某些強制化的性質下,數學家已獲得許多存在性的結果;然而,很多非線性問題格式化成變分不等式的型態時都是非強制型態.關於非強制性的變分不等式問題,近年來雖已逐漸受到研究者的重視,但可供參考的相關文獻仍非常有限.目前發現用來處理這些問題的研究大概有Attouch凹退函數理論,Leray-Schauder理論及Goeleven的判別點理論等.在本論文中,我們將沿用Attouch與Adly的凹退錐與凹退函數之概念及某些極大極小不等式,來建立一般化非強制型擬變分不等式的存在理論.

The theory of variational inequalities introduced by Stampacchia has emerged as an interesting branch of applied mathematics. This theory is a very effective tool for
studying a wide class of nonlinear problems in a unified and general framework. Several theoretical results are known under a coerciveness property, see for instance, Br´ezis, Browder, Saigal and Mosco. However, the variational formulation of many nonlinear problems leads to noncoercive variational inequalities.

Abstract
1 Introduction and basic definitions
2 Existence Theorem for Bounded Regions
3 Existence Theorem for Unbounded Regions
4 The case g(x,y)=h(y)-h(x)
References

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