Antiperiodic solutions to van der Pol equations with state-dependent impulses

dc.contributor.authorRachunkova, Irena
dc.contributor.authorTomecek, Jan
dc.date.accessioned2022-08-08T15:45:18Z
dc.date.available2022-08-08T15:45:18Z
dc.date.issued2017-10-06
dc.description.abstractIn 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.departmentMathematics
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationRachůnková, 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.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16041
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectvan der Pol equation
dc.subjectState-dependent impulses
dc.subjectExistence
dc.subjectDistributional equation
dc.subjectPeriodic distributions
dc.subjectAntiperiodic solution
dc.titleAntiperiodic solutions to van der Pol equations with state-dependent impulses
dc.typeArticle

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