Bounding function approach for impulsive Dirichlet problems with upper-Caratheodory right-hand side

Abstract

In this article, we prove the existence and localization of solutions for a vector impulsive Dirichlet problem with multivalued upper-Carath\'eodory right-hand side. The result is obtained by combining the continuation principle with a bound sets technique. The main theorem is illustrated by an application to the forced pendulum equation with viscous damping term and dry friction coefficient.