Applications of Mathematics, first online, pp. 1-12

Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions

Martina Pavlačková, Pavel Ženčák

Received September 13, 2019.   Published online October 21, 2020.

Abstract:  Sufficient conditions are given for the solvability of an impulsive Dirichlet boundary value problem to forced nonlinear differential equations involving the combination of viscous and dry frictions. Apart from the solvability, also the explicit estimates of solutions and their derivatives are obtained. As an application, an illustrative example is given, and the corresponding numerical solution is obtained by applying Matlab software.
Keywords:  impulsive Dirichlet problem; Kakutani-Ky Fan fixed-point theorem; pendulum equation; dry friction
Classification MSC:  34A60, 34B15
DOI:  10.21136/AM.2020.0232-19

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Affiliations:   Martina Pavlačková (corresponding author), Department of Computer Science and Applied Mathematics, Moravian Business College Olomouc, tř. Kosmonautů 1288/1, 779 00, Olomouc, Czech Republic, e-mail:; Pavel Ženčák, Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail:

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