Nontrivial solutions for asymptotically linear variational inequalities (Q1380890)

The aim of this paper is to extend variational inequalities a result of Amann and Zehnder's, refined by Chang, concerning the existence of nontrivial solutions for a semilinear elliptic boundary value problem, when the nonlinearity is asymptotically linear, is zero at zero and its derivative has a suitable jump between zero and infinity. In the constrained problem studied here the presence of the ``obstacle'' enters into the discussion and what determines the required ``jump of behaviour'' is a combination of the nonlinearity and the obstacle.