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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1403119
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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).


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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: http://dx.doi.org/10.1090/S0002-9939-97-03947-6
PII: S 0002-9939(97)03947-6
Received by editor(s): November 16, 1994
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society