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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, Number 3, Pages 71–90 (Mi basm180)  

This article is cited in 7 scientific papers (total in 7 papers)

Research articles

Variety of the center and limit cycles of a cubic system, which is reduced to lienard form

Yu. L. Bondar, A. P. Sadovskii

Belarussian State University, Minsk, Belarus

Abstract: In the present work for the system $\dot{x}=y(1+Dx+Px^2)$, $\dot{y}=-x+Ax^2+3Bxy+Cy^2+Kx^3+3Lx^2y+Mxy^2+Ny^3$ 25 cases are given when the point $O(0,0)$ is a center. We also consider a system of the form $\dot{x}=yP_0(x)$, $\dot{y}=-x+P_2(x)y^2+P_3(x)y^3$, for which 35 cases of a center are shown. We prove the existence of systems of the form $\dot{x}=y(1+Dx+Px^2)$, $\dot{y}=-x+\lambda y +Ax^2+Cy^2+Kx^3+3Lx^2y+Mxy^2+Ny^3$ with eight limit cycles in the neighborhood of the origin of coordinates.

Keywords and phrases: Center-focus problem, Lienard systems of differential equations, cubic systems, limit cycles, Cherkas method.

Full text: PDF file (248 kB)
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Bibliographic databases:
MSC: 34C05
Received: 12.12.2004
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Citation: Yu. L. Bondar, A. P. Sadovskii, “Variety of the center and limit cycles of a cubic system, which is reduced to lienard form”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 3, 71–90

Citation in format AMSBIB
\Bibitem{BonSad04}
\by Yu.~L.~Bondar, A.~P.~Sadovskii
\paper Variety of the center and limit cycles of a~cubic system, which is reduced to lienard form
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2004
\issue 3
\pages 71--90
\mathnet{http://mi.mathnet.ru/basm180}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2148011}
\zmath{https://zbmath.org/?q=an:1079.34019}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gheorghe Tigan, “On a family of Hamiltonian cubic planar differential systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, no. 2, 75–86  mathnet  mathscinet  zmath
    2. Differ. Equ., 44:2 (2008), 274–277  crossref  mathscinet  zmath  isi  scopus
    3. Cozma D., “The problem of the centre for cubic systems with two parallel invariant straight lines and one invariant conic”, NoDEA Nonlinear Differential Equations Appl., 16:2 (2009), 213–234  crossref  mathscinet  zmath  isi  scopus
    4. Dimitru Cozma, “Center problem for a class of cubic systems with a bundle of two invariant straight lines and one invariant conic”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2010, no. 3, 51–66  mathnet  mathscinet  zmath
    5. Differ. Equ., 47:2 (2011), 208–223  crossref  mathscinet  zmath  isi  elib  scopus
    6. Dumitru Cozma, “Center problem for cubic systems with a bundle of two invariant straight lines and one invariant conic”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 1, 32–49  mathnet  mathscinet  zmath
    7. Dimitru Cozma, Anatoli Dascalescu, “Integrability conditions for a class of cubic differential systems with a bundle of two invariant straight lines and one invariant cubic”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 1, 120–138  mathnet
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