Antiperiodic solutions to van der Pol equations with state-dependent impulses
| dc.contributor.author | Rachunkova, Irena | |
| dc.contributor.author | Tomecek, Jan | |
| dc.date.accessioned | 2022-08-08T15:45:18Z | |
| dc.date.available | 2022-08-08T15:45:18Z | |
| dc.date.issued | 2017-10-06 | |
| dc.description.abstract | In this article we give sufficient conditions for the existence of an antiperiodic solution to the van der Pol equation x′(t) = y(t), y′(t) = μ(x(t) - x3(t)/3)′ - x(t) + ƒ(t) for a. e. t ∈ ℝ, subject to a finite number of state-dependent impulses ∆y(τi(x)) = Ji(x), i = 1, …, m. Our approach is based on the reformulation of the problem as a distributional differential equation and on the Schauder fixed point theorem. The functionals τi and Ji need not be Lipschitz continuous nor bounded. As a direct consequence, we obtain an existence result for problem with fixed-time impulses. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Rachůnková, I., & Tomeček, J. (2017). Antiperiodic solutions to van der Pol equations with state-dependent impulses. <i>Electronic Journal of Differential Equations, 2017</i>(247), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16041 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | van der Pol equation | |
| dc.subject | State-dependent impulses | |
| dc.subject | Existence | |
| dc.subject | Distributional equation | |
| dc.subject | Periodic distributions | |
| dc.subject | Antiperiodic solution | |
| dc.title | Antiperiodic solutions to van der Pol equations with state-dependent impulses | |
| dc.type | Article |