A multiplicity result for a class of nonlinear variational inequalities

Abstract

We consider a class of variational inequalities and we give an existence result of a nonnegative, not identically zero solution. Such result generalizes the ones obtained by other authors through topological methods, to nonlinear variational inequalities. We also obtain the existence of at least two not identically zero solutions for a class of semilinear elliptic variational inequalities. Our proof of the existence result is based on the so called direct method, i.e., we introduce a suitable functional and we prove that it has a minimum, which is a solution of the variational inequality