×

Comment on: “Centers of quasi-homogeneous polynomial planar systems”. (English) Zbl 1373.34051

Summary: We describe a counter-example which shows that \((\mathbf{2})\) of theorem (\(\mathbf{11}\)) in [A. Algaba et al., Nonlinear Anal., Real World Appl. 13, No. 1, 419–431 (2012; Zbl 1238.34052)] is not correct. This part of the theorem, pinpoints whether the origin of quasi-homogeneous system \((\mathbf{15})\) in [loc. cit.] is a center or not. It is shown in this note that the given necessary and sufficient conditions of theorem (\(\mathbf{11}\)), in [loc. cit.] are not complete.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations

Citations:

Zbl 1238.34052
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Algaba, A.; Fuentes, N.; Garcí, C., Centers of quasi-homogeneous polynomial planar systems, Nonlinear Anal. RWA, 13, 1, 419-431 (2012) · Zbl 1238.34052
[2] Stewart, J., Multivariable Calculus (2012), Cengage Learning
[3] Bertsekas, D. P.; Nedi, A.; Ozdaglar, A. E., Convex Analysis and Optimization (2003), Athena Scientific
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.