Remark on a conjecture of Kaplan and Yorke
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- by Angelika Wörz-Busekros
- Proc. Amer. Math. Soc. 85 (1982), 381-382
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656107-6
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Abstract:
If all solutions of a system of quadratic differential equations with at least one stationary solution are bounded, then the corresponding homogeneous equation possesses a line of stationary points.References
- R. J. Dickson and L. M. Perko, Quadratic differential systems, Lockheed Research Report No. LMSC/L-56-68-1, Lockheed Palo Alto Research Lab., February 1968.
- R. J. Dickson and L. M. Perko, Bounded quadratic systems in the plane, J. Differential Equations 7 (1970), 251–273. MR 252787, DOI 10.1016/0022-0396(70)90110-5
- James L. Kaplan and James A. Yorke, Nonassociative, real algebras and quadratic differential equations, Nonlinear Anal. 3 (1979), no. 1, 49–51 (1978). MR 520470, DOI 10.1016/0362-546X(79)90033-6
- Lawrence Markus, Quadratic differential equations and non-associative algebras, Contributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, pp. 185–213. MR 0132743
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 381-382
- MSC: Primary 34C05; Secondary 58F14
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656107-6
- MathSciNet review: 656107