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Proceedings of the American Mathematical Society

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Quasilinear systems with several periodic solutions

Author: Jane Cronin
Journal: Proc. Amer. Math. Soc. 30 (1971), 107-111
MSC: Primary 34.45
MathSciNet review: 0280803
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Abstract: By using topological degree, it is proved that for a certain class of quasilinear systems of ordinary differential equations of the form

$\displaystyle \dot x = A(t)x + \epsilon \mu f(x,t,\mu ) + \mu g(x,t,\mu ) + h(t)$

where $ \epsilon,\mu $ are small parameters and A, f, g, h are periodic in t, there exist at least two periodic solutions.

References [Enhancements On Off] (What's this?)

  • [1] E. A. Coddington and N. Levinson, Perturbations of linear systems with constant coefficients possessing periodic solutions, Contributions to the Theory of Nonlinear Oscillations, vol. II, Princeton University Press, Princeton, 1952, pp. 19–35. MR 0054803
  • [2] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • [3] Jane Cronin, Fixed points and topological degree in nonlinear analysis, Mathematical Surveys, No. 11, American Mathematical Society, Providence, R.I., 1964. MR 0164101
  • [4] M. A. Krasnosel′skiĭ, Topologicheskie metody v teoriĭ nelineĭ nykh integral′nykh uravneniĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956 (Russian). MR 0096983

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Keywords: Topological degree, quasilinear systems of ordinary differential equations, periodic solutions
Article copyright: © Copyright 1971 American Mathematical Society