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.

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