`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Boundedness and stability for the damped and forced single well Duffing equation
Pages: 211 - 223, Issue 1, January 2013

doi:10.3934/dcds.2013.33.211      Abstract        References        Full text (125.4K)           Related Articles

Cyrine Fitouri - UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France (email)
Alain Haraux - UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France (email)

1 L. Amerio, Soluzioni quasi periodiche, o limitate, di sistemi differenziali non lineari quasi periodici, o limitati, Ann. Mat. Pura. Appl., 39 (1955), 97-119.       
2 M. Biroli, Sur les solutions bornés et presque péiodiques des éuations et inéuations d'éolution, Ann. Mat. Pura Appl., 93 (1972), 1-79.       
3 M. L. Cartwright and J. E. Littlewood, On non-linear differential equations of the second order, Ann. Math., 48 (1947), 472-494.       
4 C. M. Dafermos, Almost periodic processes and almost periodic solutions of evolution equations, in "Proccedings of a University of Florida International Symposium," Academic Press, 1977, 43-57.       
5 C. Fitouri, "Thesis Dissertation," ch.2, University of Zürich, 2008.
6 C. Fitouri and A. Haraux, Sharp estimates of bounded solutions to some semilinear second order dissipative equations, J. Math. Pures Appl., 92 (2009), 313-321.       
7 A. Haraux, "Nonlinear Evolution Equations: Global Behavior of Solutions," Springer-Verlag, New York, 1981.       
8 A. Haraux, "Systèmes Dynamiques Dissipatifs et Applications," Masson,Paris, 1991.       
9 A. Haraux, On the double well Duffing equation with a small bounded forcing term, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl.,29 (2005), 207-230.       
10 A. Haraux, Sharp estimates of bounded solutions to some second-order forced dissipative equations, J. Dynam. Differential Equations, 19 (2007), 915-933.       
11 W. S. Loud, On periodic solutions of Duffing's equation with damping, Journal of Mathematics and Physics,34 (1955), 173-178.       
12 W. S. Loud, Boundedness and convergence of solutions of x''+cx' +g(x) = e(t), Duke Math. J., 24 (1957), 63-72.       
13 W. S. Loud, Periodic solutions of x''+cx' +g(x) = f(t), Mem. Amer. Math. Soc., 31 (1959), 1-57.       
14 Ph. Souplet, Uniqueness and nonuniqueness results for the antiperiodic solutions of some second-order nonlinear evolution equations, Nonlinear Analysis T.M.A., 26 (1996), 1511-1525.

Go to top