Yang, Jihua; Zhang, Erli On the number of limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations. (English) Zbl 1472.34026 Nonlinear Anal., Real World Appl. 52, Article ID 103046, 10 p. (2020). In this paper, by analyzing the corresponding Picard-Fuchs equations, the authors obtain an upper bound of the number of limit cycles for a class of piecewise smooth Hamiltonian systems when they are perturbed inside discontinuous polynomials of degree \(n\) and present an example to illustrate an application of the theoretical results. Reviewer: Valery A. Gaiko (Minsk) Cited in 2 Documents MSC: 34A36 Discontinuous ordinary differential equations 34E10 Perturbations, asymptotics of solutions to ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations Keywords:piecewise smooth Hamiltonian system; Melnikov function; Picard-Fuchs equation PDFBibTeX XMLCite \textit{J. Yang} and \textit{E. Zhang}, Nonlinear Anal., Real World Appl. 52, Article ID 103046, 10 p. 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