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Generalized upper and lower solution method
for the forced Duffing equation


Author: Chengwen Wang
Journal: Proc. Amer. Math. Soc. 125 (1997), 397-406
MSC (1991): Primary 34B15, 34C25
DOI: https://doi.org/10.1090/S0002-9939-97-03947-6
MathSciNet review: 1403119
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper gives the generalized upper and lower solution method for the forced Duffing equation

\begin{displaymath}x '' + k x ' + f (t,x) = 0 ,\end{displaymath}

and obtains existence theorems for $T$-periodic solutions, where $f$ is a Carathéodory function. Our results generalize or extend some famous results obtained by Mawhin(1985), Habets(1990), Nkashama(1989) and Nieto(1990).


References [Enhancements On Off] (What's this?)

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  • 2. Habets, P., and Metzen, G., Existence of periodic solutions of Duffing equations, J. of Diff. Eqns. Vol 78(1989) $pp$. 1-32. MR 90c:34040
  • 3. Habets, P., and Sanchez, L., Periodic solutions of some Liénard equations with singularities. Proceedings of the American Mathematical Society, Vol 109(1990) $pp$. 1035-1044. MR 90k:34049
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  • 5. Mawhin, J., Points fixes, ponits critiques et probléme aux limites. Semin. Math. Sup. no. 92. Press Univ. de Montreál, 1985.
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Additional Information

Chengwen Wang
Affiliation: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China; Department of Mathematics & Computer Science, Rutgers University, Newark, New Jersey 07102
Email: chengwen@pegasus.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03947-6
Received by editor(s): November 16, 1994
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society

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