Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions. (English) Zbl 07332689

Pavlačková, Martina; Ženčák, Pavel

Appl. Math., Praha 66, No. 1, 57-68 (2021).

Summary: 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.

MSC:

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

Keywords:

impulsive Dirichlet problem; Kakutani-Ky Fan fixed-point theorem; pendulum equation; dry friction

Software:

Matlab

References:

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