The method of upper and lower solutions for perturbed n ^{th} order dfferential inclusions

Abstract

In this paper, an existence theorem for n th order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7, 8] and Agarwal et al. [1].