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On linear-quadratic dissipative control processes with time-varying coefficients
Boundedness and stability for the damped and forced single well Duffing equation
1. | UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France, France |
References:
[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.
doi: 10.1016/0362-546X(95)00012-K. |
show all references
References:
[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.
doi: 10.1016/0362-546X(95)00012-K. |
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