Quasilinear systems with several periodic solutions
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- by Jane Cronin PDF
- Proc. Amer. Math. Soc. 30 (1971), 107-111 Request permission
Abstract:
By using topological degree, it is proved that for a certain class of quasilinear systems of ordinary differential equations of the form \[ \dot x = A(t)x + \epsilon \mu f(x,t,\mu ) + \mu g(x,t,\mu ) + h(t)\] where $\epsilon ,\mu$ are small parameters and A, f, g, h are periodic in t, there exist at least two periodic solutions.References
- 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, N.J., 1952, pp. 19–35. MR 0054803
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- Jane Cronin, Fixed points and topological degree in nonlinear analysis, Mathematical Surveys, No. 11, American Mathematical Society, Providence, R.I., 1964. MR 0164101
- M. A. Krasnosel′skiĭ, Topologicheskie metody v teoriĭ nelineĭnykh integral′nykh uravneniĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956 (Russian). MR 0096983
Additional Information
- © Copyright 1971 American Mathematical Society
- 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