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Bounded perturbations of forced harmonic oscillators at resonance. (English) Zbl 0194.12003


MSC:

34D10 Perturbations of ordinary differential equations
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[1] Cesari, L., Functional analysis and periodic solutions of nonlinear differential equations, Contributions to Differential Equations, 1, 149-157 (1963) · Zbl 0132.07101
[2] Cronin, J., Fixed Points and Topological Degree in Nonlinear Analysis (1964), Providence: American Mathematical Society, Providence · Zbl 0117.34803
[3] Hale, J. K., Oscillations in Nonlinear Systems (1963), New York: McGraw-Hill, New York · Zbl 0115.07401
[4] Lazer, A. C., On Schauder’s fixed point theorem and forced second-order nonlinear oscillations, J. Math. Ana. and Appl., 21, 421-425 (1968) · Zbl 0155.14001 · doi:10.1016/0022-247X(68)90225-4
[5] Lazer, A. C., On the computation of periodic solutions of weakly nonlinear differential equations, SIAM J. Appl. Math, 15, 1158-1170 (1967) · Zbl 0173.18003 · doi:10.1137/0115099
[6] Leach, D. E., A uniqueness theorem, Notices Amer. Math. Soc., 15, 397-397 (1968)
[7] Loud, W. S.; Harris, W. A. Jr.; Sibuya, Y., Periodic solutions of nonlinear differential equations of Duffing type, Differenzial and Functional Equations, 199-224 (1967), New York: Benjamin, New York · Zbl 0162.12302
[8] Frederickson, P. O.; Lazer, A. C., Necessary and sufficient damping in a second order oscillator, J. Differential Eqs., 5, 262-270 (1969) · Zbl 0167.07902 · doi:10.1016/0022-0396(69)90042-4
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