Abstract:This paper provides a new simple proof of a recent result by C. B. Collins (Differential and Integral Equations 10 (1997), 333–356) to derive the center conditions for a class of planar cubic systems. The idea is to consider periodic solutions of a related scalar non-autonomous equation.
- M. A. M. Alwash and N. G. Lloyd, Nonautonomous equations related to polynomial two-dimensional systems, Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 129–152. MR 890049, DOI 10.1017/S0308210500021971
- C.B. Collins, Conditions for a center in a simple class of cubic system, Differential and Integral Equations, 10(2)(1997), 333-356.
- M. A. M. Alwash
- Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
- Email: firstname.lastname@example.org
- Received by editor(s): April 1, 1997
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3335-3336
- MSC (1991): Primary 34C25; Secondary 34C05, 34C23
- DOI: https://doi.org/10.1090/S0002-9939-98-04715-7
- MathSciNet review: 1485453