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The existence of periodic solutions for nonlinearly perturbed conservative systems. (English) Zbl 0434.34031


MSC:

34C25 Periodic solutions to ordinary differential equations
35B10 Periodic solutions to PDEs
47H10 Fixed-point theorems
34A34 Nonlinear ordinary differential equations and systems
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References:

[1] Ahmad, S., An existence theorem for periodically perturbed conservative systems, Mich. math. J., 20, 385-392 (1973) · Zbl 0294.34029
[2] Lazer, A. C., Application of a lemma on bilinear forms to a problem in nonlinear oscillations, Proc. Am. math. Soc., 33, 89-94 (1972) · Zbl 0257.34041
[3] Loud, W. S., Periodic solutions of nonlinear differential equations of Duffing type, (Proc. U.S.-Japan Seminar on Differential and functional Equations (1967), Benjamin: Benjamin New York) · Zbl 0162.12302
[4] Leach, D. E., On Poincare’s perturbation theorem and a theorem of W.S. Loud, J. diff. Eqns, 7, 34-53 (1970) · Zbl 0186.15501
[5] Lazer, A. C.; Sánchez, D. A., On periodically perturbed conservative systems, Mich. Math. J., 16, 193-200 (1969) · Zbl 0187.34501
[6] Ward, J. R., Periodic solutions of perturbed conservative systems, Proc. Am. Math. Soc., 72, 281-285 (1978) · Zbl 0418.34045
[7] BatesJ. diff. Eqns; BatesJ. diff. Eqns
[8] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602
[9] Lloyd, N. G., Degree Theory (1978), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0367.47001
[10] Chow, S.-N.; Lasota, A., On boundary value problems for ordinary differential equations, J. diff. Eqns, 14, 326-337 (1973) · Zbl 0285.34009
[11] Reid, W. T., Some elementary properties of proper values and proper vectors of matrix functions, SIAM J. appl. Math., 18, 259-266 (1970) · Zbl 0192.37201
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