On a class of second order differential inclusions driven by the scalar [formula omitted]-Laplacian

Abstract

In this paper, we study a class of nonlinear value boundary problems for second order differential inclusions. By using the methods of upper–lower solutions, truncations and penalization, we give some existence results of the extremal (greatest and smallest) solutions. Our approach is based on the theories of fixed points, maximal monotone operators and ordered Banach spaces.