| Title:
|
Dirichlet boundary value problem for an impulsive forced pendulum equation with viscous and dry frictions (English) |
| Author:
|
Pavlačková, Martina |
| Author:
|
Ženčák, Pavel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
57-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
impulsive Dirichlet problem |
| Keyword:
|
Kakutani-Ky Fan fixed-point theorem |
| Keyword:
|
pendulum equation |
| Keyword:
|
dry friction |
| MSC:
|
34A60 |
| MSC:
|
34B15 |
| idZBL:
|
07332689 |
| idMR:
|
MR4218602 |
| DOI:
|
10.21136/AM.2020.0232-19 |
| . |
| Date available:
|
2021-01-28T09:58:47Z |
| Last updated:
|
2023-03-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148510 |
| . |
| Reference:
|
[1] Andres, J., Machů, H.: Dirichlet boundary value problem for differential equations involving dry friction.Bound. Value Probl. 2015 (2015), Article ID 106, 17 pages. Zbl 1341.34018, MR 3359755, 10.1186/s13661-015-0371-z |
| Reference:
|
[2] Benedetti, I., Obukhovskii, V., Taddei, V.: On noncompact fractional order differential inclusions with generalized boundary condition and impulses in a Banach space.J. Funct. Spaces 2015 (2015), Article ID 651359, 10 pages. Zbl 1325.34007, MR 3335453, 10.1155/2015/651359 |
| Reference:
|
[3] Cecchi, M., Furi, M., Marini, M.: On continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals.Nonlinear Anal., Theory Methods Appl. 9 (1985), 171-180. Zbl 0563.34018, MR 777986, 10.1016/0362-546X(85)90070-7 |
| Reference:
|
[4] Chen, H., Li, J., He, Z.: The existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses.Appl. Math. Modelling 37 (2013), 4189-4198. Zbl 1279.34053, MR 3020563, 10.1016/j.apm.2012.09.023 |
| Reference:
|
[5] Filippov, A. F.: Differential Equations with Discontinuous Right-Hand Sides.Mathematics and Its Applications: Soviet Series 18. Kluwer Academic, Dordrecht (1988). Zbl 0664.34001, MR 0790682 |
| Reference:
|
[6] Fučík, S.: Solvability of Nonlinear Equations and Boundary Value Problems.Mathematics and Its Applications 4. D. Reidel, Dordrecht (1980). Zbl 0453.47035, MR 0620638 |
| Reference:
|
[7] Granas, A., Dugundji, J.: Fixed Point Theory.Springer Monographs in Mathematics. Springer, Berlin (2003). Zbl 1025.47002, MR 1987179, 10.1007/978-0-387-21593-8 |
| Reference:
|
[8] Hamel, G.: Über erzwungene Schwingungen bei endlichen Amplituden.Math. Ann. 86 (1922), 1-13 German \99999JFM99999 48.0519.03. MR 1512073, 10.1007/BF01458566 |
| Reference:
|
[9] Kong, F.: Subharmonic solutions with prescribed minimal period of a forced pendulum equation with impulses.Acta Appl. Math. 158 (2018), 125-137. Zbl 1407.34055, MR 3869474, 10.1007/s10440-018-0177-y |
| Reference:
|
[10] Mawhin, J.: Global results for the forced pendulum equation.Handbook of Differential Equations: Ordinary Differential Equations. Vol. 1 Elsevier, Amsterdam (2004), 533-589. Zbl 1091.34019, MR 2166494, 10.1016/S1874-5725(00)80008-5 |
| Reference:
|
[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. Zbl 0868.26003, MR 1376419 |
| Reference:
|
[12] Pavlačková, M.: A Scorza-Dragoni approach to Dirichlet problem with an upperCarathéodory right-hand side.Topol. Methods Nonlinear Anal. 44 (2014), 239-247. Zbl 1360.34031, MR 3289017, 10.12775/TMNA.2014.045 |
| Reference:
|
[13] Rachůnková, I., Tomeček, J.: Second order BVPs with state dependent impulses via lower and upper functions.Cent. Eur. J. Math. 12 (2014), 128-140. Zbl 1302.34049, MR 3121827, 10.2478/s11533-013-0324-7 |
| Reference:
|
[14] Xie, J., Luo, Z.: Subharmonic solutions with prescribed minimal period of an impulsive forced pendulum equation.Appl. Math. Lett. 52 (2016), 169-175. Zbl 1380.34065, MR 3416402, 10.1016/j.aml.2015.09.006 |
| . |
