Generalized upper and lower solution method for the forced Duffing equation

Wang, Chengwen

doi:10.1090/S0002-9939-97-03947-6

Generalized upper and lower solution method for the forced Duffing equation
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by Chengwen Wang

Proc. Amer. Math. Soc. 125 (1997), 397-406

DOI: https://doi.org/10.1090/S0002-9939-97-03947-6

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Abstract:

This paper gives the generalized upper and lower solution method for the forced Duffing equation \[ x '' + k x ’ + f (t,x) = 0 ,\] and obtains existence theorems for $T$-periodic solutions, where $f$ is a Carathéo- dory function. Our results generalize or extend some famous results obtained by Mawhin(1985), Habets(1990), Nkashama(1989) and Nieto(1990).

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