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Bounding function approach for impulsive Dirichlet problems with upper-Carathéodory right-hand side. (English) Zbl 1406.34052

Summary: In this article, we prove the existence and localization of solutions for a vector impulsive Dirichlet problem with multivalued upper-Carathéodory 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.

MSC:

34A60 Ordinary differential inclusions
34B15 Nonlinear boundary value problems for ordinary differential equations
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