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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
DOI: https://doi.org/10.1090/S0002-9939-1971-0280803-9
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. 2, Princeton Univ. Press, Princeton, N. J., 1952, pp. 19-35. MR 14, 981. MR 0054803 (14:981f)
  • [2] -, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 16, 1022. MR 0069338 (16:1022b)
  • [3] J. Cronin, Fixed points and topological degree in nonlinear analysis, Math. Surveys, no. 11, Amer. Math. Soc., Providence, R. I., 1964. MR 29 #1400. MR 0164101 (29:1400)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0280803-9
Keywords: Topological degree, quasilinear systems of ordinary differential equations, periodic solutions
Article copyright: © Copyright 1971 American Mathematical Society

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