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On the center conditions of certain cubic systems

Author(s): M. A. M. Alwash
Journal: Proc. Amer. Math. Soc. 126 (1998), 3335-3336.
MSC (1991): Primary 34C25; Secondary 34C05, 34C23
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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.

References:

[1]
M.A.M. Alwash and N.G. Lloyd, Non-autonomous equations related to polynomial two-dimensional systems, Proc. Royal Soc. Edinburgh, 105A(1987), 129-152. MR 88i:58145
[2]
C.B. Collins, Conditions for a center in a simple class of cubic system, Differential and Integral Equations, 10(2)(1997), 333-356. CMP 97:05

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Additional Information:

M. A. M. Alwash
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
Email: alwash@math.ucla.edu

DOI: 10.1090/S0002-9939-98-04715-7
PII: S 0002-9939(98)04715-7
Received by editor(s): April 1, 1997
Communicated by: Hal L. Smith
Copyright of article: Copyright 1998, American Mathematical Society

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