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Remark on a conjecture of Kaplan and Yorke

Author: Angelika Wörz-Busekros
Journal: Proc. Amer. Math. Soc. 85 (1982), 381-382
MSC: Primary 34C05; Secondary 58F14
MathSciNet review: 656107
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] -, Bounded quadratic systems in the plane, J. Differential Equations 7 (1970), 251-273. MR 0252787 (40:6004)
  • [3] J. L. Kaplan and J. A. Yorke, Nonassociative, real algebras and quadratic differential equations, Nonlinear Anal., Theory, Methods and Appl. 3 (1979), 49-51. MR 520470 (80d:58060)
  • [4] L. Markus, Quadratic differential equations and nonassociative algebras, Contributions to the Theory of Nonlinear Oscillations (L. Cesari, J. LaSalle, S. Lefschetz (eds.)), Princeton Univ. Press, Princeton, N.J., 1960, pp. 185-213. MR 0132743 (24:A2580)

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Keywords: Inhomogeneous, homogeneous quadratic differential equations
Article copyright: © Copyright 1982 American Mathematical Society

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