A variational method for the existence of bounded solutions of a sublinear forced oscillator

Proceedings of the London Mathematical Society

Volumn 88, Issue 3, 2004, Pages 775-795

  Ortega, Rafael ^a   Verzini, Gianmaria ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442700406     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611503014515     Document Type: Conference Paper

References (17)

1. A. AMBROSETTI and G. PRODI, A primer of non-linear analysis (Cambridge University Press, 1995).
2. T. DING, Review 93d:34064, MR (1993).
3. T. DING and F. ZANOLIN, 'Subharmonic solutions of second order non-linear equations: a time-map approach', Nonlinear Anal. 20 (1993) 509-532.
4. A. FONDA and M. RAMOS, 'Large-amplitude subharmonic oscillations for scalar second-order differential equations with asymmetric non-linearities', J. Differential Equations 109 (1994) 354-372.
5. I. M. GELFAND and S. V. FOMIN, Calculus of variations (Prentice-Hall, Englewood Cliffs, NJ, 1963).
6. T. KÜPPER and J. You, 'Existence of quasiperiodic solutions and Littlewood's boundedness problem of Duffing equations with subquadratic potentials', Nonlinear Anal. 35 (1999) 549-559.
7. M. LEVI and E. ZEHNDER, 'Boundedness of solutions for quasiperiodic potentials', SIAM J. Math. Anal. 26 (1995) 1233-1256.
8. J. E. LITTLEWOOD, 'Unbounded solutions of ÿ + g(y) = p(t)', J. London Math. Soc. 41 (1966) 491-496.
9. J. E. LITTLEWOOD, 'Unbounded solutions of an equation ÿ + g(y) = p(t), with p(t) periodic and bounded, and g(y)/y → as y → +±∞', J. London Math. Soc. 41 (1966) 497-507.
10. B. LIU, 'On Littlewood's boundedness problem for sublinear Duffing equations', Trans. Amer. Math. Soc. 353 (2001) 1567-1585.
11. B. LIU and F. ZANOLIN, 'Boundedness of solutions for second order quasilinear ODEs', Preprint, University of Beijing, 1996.
12. Y. LONG, 'An unbounded solution of a superlinear Duffing's equation', Acta Math. Sinica (N.S.) 7 (1991) 360-369.
13. G. MORRIS, 'A case of boundedness of Littlewood's problem on oscillatory differential equations', Bull. Austral. Math. Soc. 14 (1976) 71-93.
14. Z. NEHARI, 'Characteristic values associated with a class of non-linear second order differential equations', Acta Math. 105 (1961) 141-175.
15. J. W. NORRIS, 'Boundedness in periodically forced second order conservative systems', J. London Math. Soc. (2) 45 (1992) 97-112.
16. S. TERRACINI and G VERZINI, 'Oscillating solutions to second order ODE's with indefinite superlinear nonlinearities', Nonlinearity 13 (2000) 1501-1514.
17. G. VERZINI, 'Bounded solutions to superlinear ODEs: a variational approach', Nonlinearity 16 (2003) 2013-2028.