Asymptotical multiplicity and some reversed variational inequalities

Abstract

We are concerned with multiplicity results for solutions of some reversed variational inequalities, in which the inequality is opposite with respect to the classical inequalities introduced by Lions and Stampacchia. The inequalities we study arise from a family (P$_\omega$) of elliptic problems of the fourth order when $\omega$ tends to $\infty$. We use two basic tools: the $\nabla$-theorems and a theorem about the multiplicity of "asymptotically critical" points. In the last section some open problems are listed.