Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, \cyr Topologicheskie metody v teoriĭ nelineĭnykh integral′nykh uravneniĭ., Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956 (Russian). MR 0096983

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.45

Retrieve articles in all journals with MSC: 34.45


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