Electron. J. Differential Equations, Vol. 2019 (2019), No. 12, pp. 1-18.

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

Martina Pavlackova, Valentina Taddei

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.

Submitted May 28, 2018. Published January 24, 2019.
Math Subject Classifications: 34A60, 34B15.
Key Words: Impulsive Dirichlet problem; bounding function; upper-Caratheodory differential inclusions.

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Martina Pavlačková
Dept. of Math. Analysis and Appl. of Mathematics
Fac. of Science, Palacký University
17. listopadu 12
771 46 Olomouc, Czech Republic
email: martina.pavlackova@upol.cz
Valentina Taddei
Dept. of Sciences and Methods for Engineering
University of Modena and Reggio Emilia
Via G. Amendola, 2 - pad. Morselli
I-42122 Reggio Emilia, Italy
email: valentina.taddei@unimore.it

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