On solvability of variational inequalities with discontinuous semimonotone operators - Pavlenko, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
By using the method of monotone operators, a theorem on the existence of the solution with a special property is obtained for an elliptic variational inequality with discontinuous semimonotone operator; this theorem is then used to prove the existence of a semicorrect solution of a variational inequality with a differential semilinear high-order operator of elliptic type with a nonsymmetric linear part and discontinuous nonlinearity.