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Resonant forced oscillations in systems with periodic nonlinearities
1. | Institute for Information Transmission Problems, 19 Bolshoi Karetny, 127994, GSP-4 Moscow, Russian Federation |
References:
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doi: 10.1088/0951-7715/9/5/003. |
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V. I. Arnold, "Arnold's Problems,'' Problem 1996-5, comments by S.B.Kuksin, Springer-Verlag, New York, (2005), 580-582. |
[3] |
D. Bonheure, C. Fabry and D. Ruiz, Problems at resonance for equations with periodic nonlinearities, Nonlinear Analysis, 55 (2003), 557-581.
doi: 10.1016/j.na.2003.07.005. |
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A. Cańada and F. Roca, Existence and multiplicity of solutions of someconservative pendulum-type equations with homogeneous Dirichlet conditions, Diff. and Int. Eq., 10 (1997), 1113-1122. |
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E. N. Dancer, On the use of asymptotics in nonlinear boundary value problems, Ann. Mat. Pura Appl., 131 (1982), 167-185.
doi: 10.1007/BF01765151. |
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A. Isidori, "Nonlinear Control Systems,'' Springer-Verlag, London, 1995. |
[7] |
H. K. Khalil, "Nonlinear Systems,'' Prentice Hall, Upper Saddle River, New Jersey, 2002. |
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A. M. Krasnosel'skii and M. A. Krasnosel'skii, Vector fields in the direct product of spaces, and applications todifferential equations, Differential Equations, 33 (1997), 59-66. |
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A. M. Krasnosel'skii and J. Mawhin, The index at infinity of some twice degenerate compact vector fields, Discrete Contin. Dyn. Syst., 1 (1995), 207-216.
doi: 10.3934/dcds.1995.1.207. |
[10] |
A. M. Krasnosel'skii and J. Mawhin, Periodic solutions of equations with oscillating nonlinearities, Mathematical and Computer Modelling, 32 (2000), 1445-1455
doi: 10.1016/S0895-7177(00)00216-8. |
[11] |
M. A. Krasnosel'skii and P. P. Zabreiko, "Geometrical Methods of Nonlinear Analysis,'' Springer-Verlag, Berlin, Heidelberg, 1984. |
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F. W. S. Olver, "Asymptotics and Special Functions,'' Academic Press, New York, 1974. |
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G. Pólya and G. Szegö, "Aufgaben and Lehrsätze aus der Analysis,'' Springer, Berlin, B I-II (1925). |
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R. Schaaf and K. Schmitt, A class of nonlinear Sturm-Liouville problems with infinitely many solutions, Trans. Amer. Math. Soc., 306 (1988), 853-859.
doi: 10.1090/S0002-9947-1988-0933322-5. |
show all references
References:
[1] |
J. M. Alonso and R. Ortega, Unbounded solutions of semilinear equations at resonance, Nonlinearity, 9 (1996), 1099-1111.
doi: 10.1088/0951-7715/9/5/003. |
[2] |
V. I. Arnold, "Arnold's Problems,'' Problem 1996-5, comments by S.B.Kuksin, Springer-Verlag, New York, (2005), 580-582. |
[3] |
D. Bonheure, C. Fabry and D. Ruiz, Problems at resonance for equations with periodic nonlinearities, Nonlinear Analysis, 55 (2003), 557-581.
doi: 10.1016/j.na.2003.07.005. |
[4] |
A. Cańada and F. Roca, Existence and multiplicity of solutions of someconservative pendulum-type equations with homogeneous Dirichlet conditions, Diff. and Int. Eq., 10 (1997), 1113-1122. |
[5] |
E. N. Dancer, On the use of asymptotics in nonlinear boundary value problems, Ann. Mat. Pura Appl., 131 (1982), 167-185.
doi: 10.1007/BF01765151. |
[6] |
A. Isidori, "Nonlinear Control Systems,'' Springer-Verlag, London, 1995. |
[7] |
H. K. Khalil, "Nonlinear Systems,'' Prentice Hall, Upper Saddle River, New Jersey, 2002. |
[8] |
A. M. Krasnosel'skii and M. A. Krasnosel'skii, Vector fields in the direct product of spaces, and applications todifferential equations, Differential Equations, 33 (1997), 59-66. |
[9] |
A. M. Krasnosel'skii and J. Mawhin, The index at infinity of some twice degenerate compact vector fields, Discrete Contin. Dyn. Syst., 1 (1995), 207-216.
doi: 10.3934/dcds.1995.1.207. |
[10] |
A. M. Krasnosel'skii and J. Mawhin, Periodic solutions of equations with oscillating nonlinearities, Mathematical and Computer Modelling, 32 (2000), 1445-1455
doi: 10.1016/S0895-7177(00)00216-8. |
[11] |
M. A. Krasnosel'skii and P. P. Zabreiko, "Geometrical Methods of Nonlinear Analysis,'' Springer-Verlag, Berlin, Heidelberg, 1984. |
[12] |
F. W. S. Olver, "Asymptotics and Special Functions,'' Academic Press, New York, 1974. |
[13] |
G. Pólya and G. Szegö, "Aufgaben and Lehrsätze aus der Analysis,'' Springer, Berlin, B I-II (1925). |
[14] |
R. Schaaf and K. Schmitt, A class of nonlinear Sturm-Liouville problems with infinitely many solutions, Trans. Amer. Math. Soc., 306 (1988), 853-859.
doi: 10.1090/S0002-9947-1988-0933322-5. |
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