Sub-Supersolution Method For Hemi-variational Inequalities And Its Application

In this thesis, we study a class of higher quasi-linear elliptic hemi-variational inequalities, define its subsolution,supersolution and extremal solution and generalize the sub-supersolution method to this class of quasi-linear elliptic hemi-variational inequalities. By using sub-supersolution method, we prove the existence of solutions and extremal solutions and the compactness of solutions between subsolution and supersolution for the higher order quasi-linear elliptic hemi-variational inequality under considerations. At last, by applying our obtained results we prove the existence of solutions and extremal solutions and the compactness of solutions between subsolution and supersolutions for a class of hemi-variational inequality involving p-Laplacian operator.