Rachunkova, IrenaTomecek, Jan2022-08-082022-08-082017-10-06Rachůnková, 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. 1-17.1072-6691https://hdl.handle.net/10877/16041In 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.Text18 pages1 file (.pdf)enAttribution 4.0 Internationalvan der Pol equationState-dependent impulsesExistenceDistributional equationPeriodic distributionsAntiperiodic solutionArticle