Behavior of forced asymmetric oscillators at resonance

Electronic Journal of Differential Equations

Volumn 2000, Issue , 2000, Pages

  Fabry, C ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Frequency response curves; Fuc k spectrum; Jumping nonlinearity; Resonance

Indexed keywords

EID: 52849098156     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. J. M. Alonso and R. Ortega, Roots of unity and unbounded motions of an asymmetric oscillator, J. Differential Equations, 143 (1998), 201-220.
2. E. N. Dancer, Boundary-value problems for weakly nonlinear ordinary differential equations, Bull. Austral. Math. Soc. 15 (1976), 321-328.
3. E. N. Dancer, Proofs of the results in "Boundary-value problems for weakly nonlinear ordinary differential equations", unpublished.
4. C. Fabry, Aspects of resonance in nonlinear oscillators, to appear.
5. C. Fabry, Large-amplitude oscillations of a nonlinear asymmetric oscillator with damping, Nonlinear Anal., to appear.
6. C. Fabry, A. Fonda, Nonlinear resonance in asymmetric oscillators, J. Differential Equations, 147 (1998), 58-78.
7. C. Fabry, A. Fonda, Bifurcations from infinity in asymmetric nonlinear oscillators, NoDEA 7 (2000), 23-42.
8. C. Fabry, J. Mawhin, Oscillations of a forced asymmetric oscillator at resonance, Nonlinearity, 13 (2000), 493-505.
9. S. Fucik, Boundary value problems with jumping nonlinearities, Casopis pro pest. mat. 101 (1976), 69-87.
10. S. Fucik, Solvability of Nonlinear Equations and Boundary Value Problems, Reidel, Boston, 1980.
11. A. C. Lazer and P. J. McKenna, Existence, uniqueness, and stability of oscillations in differential equations with asymmetric nonlinearities, Trans. Amer. Math. Soc., 315 (1989), 721-739.
12. A. C. Lazer and P. J. McKenna, Large-amplitude periodic oscillations in suspension bridges : some new connections with nonlinear analysis, SIAM Rev. 32 (1990), 537-578.
13. Liu Bin, Boundedness in asymmetric oscillations, J. Math. Anal. Appl. 231 (1999), 355-373.
14. J. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J., 17 (1950), 457-475.
15. R. Ortega, Asymmetric oscillators and twist mappings, J. London Math. Soc. 53(1996), 325-342.
16. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, Berlin, 1990.
17. Wang Zaihong, Periodic solutions of the second order differential equations with jumping nonlinearities, to appear.