Discontinuous Variational-Hemivariational Inequalities Involving the ρ-Laplacian.

The article presents a research on the discontinuous quasilinear elliptic variational-hemivariational inequalities which involves the ρ-Laplacian. It also notes on the extension of the theory for discontinuous problems with the use of the method of sub- and supersolutions and compared on the results of S. Carl. It also aims to prove the existence of extremal solutions within a given order interval of sub- and supersolutions. It also gives example of the construction of sub- and supersolutions.