On the Semi-monotone Operator Theory and Applications

In this paper, E is a real Banach space, A : E**=E**ªE* is a semi-monotone operator. We first study the variational inequality problem: Find ugK, such that A u, u., ¨ yu.G0, where K;E** is a closed convex subset; then the operator equation A u, u.sp*, and we also construct a degree theory for demicontinuous semi-monotone operators in reflexive Banach spaces.