Abstract
In this paper,Eis a real Banach space,A:E**×E**→E* is a semi-monotone operator. We first study the variational inequality problem: Findu∈K, such that (A(u,u),v−u)≥0, whereK⊂E** is a closed convex subset; then the operator equationA(u,u)=p*, and we also construct a degree theory for demi-continuous semi-monotone operators in reflexive Banach spaces.
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