A variational inequality index for condensing maps in Hilbert spaces and applications to semilinear elliptic inequalities Original Research Article

A variational inequality index for γγ-condensing maps is established in Hilbert spaces. New results on existence of nonzero positive solutions of variational inequalities for such maps are proved by using the theory of variational inequality index. Applications of such a theory are given to existence of nonzero positive weak solutions for semilinear second order elliptic inequalities, where previous results of variational inequalities for SS-contractive maps cannot be applied.