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

Martina Pavlačková; Pavel Ženčák

Applications of Mathematics (2021)

  • Volume: 66, Issue: 1, page 57-68
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Pavlačková, Martina, and Ženčák, Pavel. "Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions." Applications of Mathematics 66.1 (2021): 57-68. <http://eudml.org/doc/296969>.

@article{Pavlačková2021,
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.},
author = {Pavlačková, Martina, Ženčák, Pavel},
journal = {Applications of Mathematics},
keywords = {impulsive Dirichlet problem; Kakutani-Ky Fan fixed-point theorem; pendulum equation; dry friction},
language = {eng},
number = {1},
pages = {57-68},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions},
url = {http://eudml.org/doc/296969},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Pavlačková, Martina
AU - Ženčák, Pavel
TI - Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 57
EP - 68
AB - 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.
LA - eng
KW - impulsive Dirichlet problem; Kakutani-Ky Fan fixed-point theorem; pendulum equation; dry friction
UR - http://eudml.org/doc/296969
ER -

References

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  1. Andres, J., Machů, H., 10.1186/s13661-015-0371-z, Bound. Value Probl. 2015 (2015), Article ID 106, 17 pages. (2015) Zbl1341.34018MR3359755DOI10.1186/s13661-015-0371-z
  2. Benedetti, I., Obukhovskii, V., Taddei, V., 10.1155/2015/651359, J. Funct. Spaces 2015 (2015), Article ID 651359, 10 pages. (2015) Zbl1325.34007MR3335453DOI10.1155/2015/651359
  3. Cecchi, M., Furi, M., Marini, M., 10.1016/0362-546X(85)90070-7, Nonlinear Anal., Theory Methods Appl. 9 (1985), 171-180. (1985) Zbl0563.34018MR777986DOI10.1016/0362-546X(85)90070-7
  4. Chen, H., Li, J., He, Z., 10.1016/j.apm.2012.09.023, Appl. Math. Modelling 37 (2013), 4189-4198. (2013) Zbl1279.34053MR3020563DOI10.1016/j.apm.2012.09.023
  5. Filippov, A. F., Differential Equations with Discontinuous Right-Hand Sides, Mathematics and Its Applications: Soviet Series 18. Kluwer Academic, Dordrecht (1988). (1988) Zbl0664.34001MR0790682
  6. Fučík, S., Solvability of Nonlinear Equations and Boundary Value Problems, Mathematics and Its Applications 4. D. Reidel, Dordrecht (1980). (1980) Zbl0453.47035MR0620638
  7. Granas, A., Dugundji, J., 10.1007/978-0-387-21593-8, Springer Monographs in Mathematics. Springer, Berlin (2003). (2003) Zbl1025.47002MR1987179DOI10.1007/978-0-387-21593-8
  8. Hamel, G., 10.1007/BF01458566, Math. Ann. 86 (1922), 1-13 German 9999JFM99999 48.0519.03. (1922) MR1512073DOI10.1007/BF01458566
  9. Kong, F., 10.1007/s10440-018-0177-y, Acta Appl. Math. 158 (2018), 125-137. (2018) Zbl1407.34055MR3869474DOI10.1007/s10440-018-0177-y
  10. Mawhin, J., 10.1016/S1874-5725(00)80008-5, Handbook of Differential Equations: Ordinary Differential Equations. Vol. 1 Elsevier, Amsterdam (2004), 533-589. (2004) Zbl1091.34019MR2166494DOI10.1016/S1874-5725(00)80008-5
  11. Meneses, J., Naulin, R., Ascoli-Arzelá theorem for a class of right continuous functions, Ann. Univ. Sci. Budap. Eötvös, Sect. Math. 38 (1995), 127-135. (1995) Zbl0868.26003MR1376419
  12. Pavlačková, M., 10.12775/TMNA.2014.045, Topol. Methods Nonlinear Anal. 44 (2014), 239-247. (2014) Zbl1360.34031MR3289017DOI10.12775/TMNA.2014.045
  13. Rachůnková, I., Tomeček, J., 10.2478/s11533-013-0324-7, Cent. Eur. J. Math. 12 (2014), 128-140. (2014) Zbl1302.34049MR3121827DOI10.2478/s11533-013-0324-7
  14. Xie, J., Luo, Z., 10.1016/j.aml.2015.09.006, Appl. Math. Lett. 52 (2016), 169-175. (2016) Zbl1380.34065MR3416402DOI10.1016/j.aml.2015.09.006

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