Existence of quasiperiodic solutions and Littlewood's boundedness problem of Duffing equations with subquadratic potentials

Nonlinear Analysis, Theory, Methods and Applications

Volumn 35, Issue 5, 1999, Pages 549-559

  Küpper, Tassilo ^a   You, Jiangong ^b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b NANJING UNIVERSITY   (China)

Author keywords

Littlewood's boundedness problem; Subquadratic potential

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

DUFFING EQUATION; LITTLEWOOD'S BOUNDEDNESS PROBLEM; SUBQUADRATIC POTENTIAL;

NONLINEAR EQUATIONS;

EID: 0033101765     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00709-8     Document Type: Article

References (13)

1. Arnol'd A.I. Mathematical Methods of Classical Mechanics. 1978;Springer, Berlin.
2. J. Andres, Several remarks to problem of Moser and conjecture of Mawhin, Bodlettino U.M.I. 7 7-A (1993) 377-386.
3. Diekerhoff R., Zehnder E. Boundedness for solutions via the twist theorem. Ann. Scuola Norm. Sup. Pisa. 14:1987;79-95.
4. M.R. Herman, Sur les courbes invariantes par les diffeormorphismes de I'anneau, Asterisque 144 (1986) .
5. J. Littlewood, Some Problems in Real and Complex Analysis, Heath, Lexington, MA, 1968 .
6. B. Liu, Boundedness for solutions of nonlinear Hill's equation with periodic forcing terms via Moser's twist theorem. J. Differential Eqs. 9 (2) (1989) .
7. Levi M. Quasiperiodic motions in superquadratic time periodic potentials. Commun. Math. Phys. 143(1):1991;43-83.
8. J. Mawhin, Willem, Critical point theory and Hamiltonian, Applied Mathematical Sciences, vol. 55, Springer, Berlin, 1989.
9. G. Morris, A case of the boundedness in Littlewood's problem on oscillatory differential equations, Bull. Austr. Math. Soc. 14 (1976).
10. J. Moser, On invariant curves of area preserving mappings of an annulus, Nachr. Akad. Wiss. Gottingen Math-Phys. Kl.II (1962) .
11. J.W. Norris, Boundedness in periodically forced second order conservative systems, J. London Math. Soc. 45 (1992) .
12. 2 time dependent coefficient, ZAMP 47 (6) (1996) .
13. J. You, Boundedness for solutions of superlinear Duffing equations via the twist theorem, Sci. China Scientia Sinica 35 (4) (1992) .