A multiplicity result for a class ofnonlinear variational inequalities

  • Raffaella Servadei
  • Enrico Valdinoci


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 in [4] and [9], which were obtained by 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 which have been studied in [4] and [9]. 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. The proof of the multiplicity result follows from [4], [9] and suitable functional estimates.