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Periodic solutions of perturbed conservative systems. (English) Zbl 0418.34045


MSC:

34C25 Periodic solutions to ordinary differential equations
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References:

[1] Shair Ahmad, An existence theorem for periodically perturbed conservative systems, Michigan Math. J. 20 (1973), 385 – 392. · Zbl 0294.34029
[2] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. · Zbl 0064.33002
[3] R. Kannan, Periodically perturbed conservative systems, J. Differential Equations 16 (1974), no. 3, 506 – 514. · Zbl 0349.34029 · doi:10.1016/0022-0396(74)90006-0
[4] M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, Translated by A. H. Armstrong; translation edited by J. Burlak. A Pergamon Press Book, The Macmillan Co., New York, 1964.
[5] A. C. Lazer, Application of a lemma on bilinear forms to a problem in nonlinear oscillations, Proc. Amer. Math. Soc. 33 (1972), 89 – 94. · Zbl 0257.34041
[6] A. C. Lazer and D. A. Sánchez, On periodically perturbed conservative systems, Michigan Math. J. 16 (1969), 193 – 200. · Zbl 0187.34501
[7] D. E. Leach, On Poincaré’s perturbation theorem and a theorem of W. S. Loud, J. Differential Equations 7 (1970), 34 – 53. · Zbl 0186.15501 · doi:10.1016/0022-0396(70)90122-1
[8] W. S. Loud, Periodic solutions of nonlinear differential equations of Duffing type, Proc. U.S.-Japan Seminar on Differential and Functional Equations (Minneapolis, Minn., 1967) Benjamin, New York, 1967, pp. 199 – 224. · Zbl 0162.12302
[9] Jean Mawhin, Contractive mappings and periodically perturbed conservative systems, Arch. Math. (Brno) 12 (1976), no. 2, 67 – 73. · Zbl 0353.47034
[10] Rolf Reissig, Contractive mappings and periodically perturbed non-conservative systems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), no. 5, 696 – 702 (English, with Italian summary). · Zbl 0344.34033
[11] D. A. Smart, Fixed point theorems, Cambridge Univ. Press, Cambridge, 1975. · Zbl 0427.47036
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