Sub–supersolution method and extremal solutions for higher order quasi-linear elliptic hemi-variational inequalities

In the present paper, we generalize the sub–supersolution method for a class of higher order quasi-linear elliptic hemi-variational inequalities. Using the notion of sub and supersolution, we prove the existence, comparison, compactness and extremality results for the higher order quasi-linear elliptic hemi-variational inequality under considerations.