Existence of solutions to initial value problems for the second order mixed monotone type of impulsive differential inclusions

Abstract

In this paper we consider the initial value problems for the second order mixed monotone type of impulsive differential inclusions. By introducing a special partial order, we present the existence of maximal and minimal fixed points for mixed monotone multivalued operators in Banach spaces. Applying the results, we establish the existence and uniqueness of above impulsive differential inclusions.