Evolution inequalities with noncoercive $w_{{{\rm{\lambda}}_{0}}}$ -pseudomonotone volterra-type mappings

Abstract

We consider a class of differential-operator inequalities with noncoercive $w_{{{\rm{\lambda}}_{0}}}$ -pseudomonotone operators. The problem of existence of a solution of the Cauchy problem for these inequalities is investigated by the Dubinskii method. A priori estimates for these solutions and their derivatives are established. A model example illustrating the accumulated results is presented.