Asymptotical multiplicity and some reversed variational inequalities

We are concerned with multiplicity results for solutions of somereversed variational inequalities, in which the inequality is oppositewith respect to the classical inequalities introduced by Lions andStampacchia. 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 anda theorem about the multiplicity of ``asymptotically critical''points. In the last section some open problems are listed.