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Multiplicity of periodic solutions for Duffing equations under nonuniform non-resonance conditions

Author(s): Chengwen Wang
Journal: Proc. Amer. Math. Soc. 126 (1998), 1725-1732.
MSC (1991): Primary 34C25, 34B15
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Abstract: This paper is devoted to the study of multiple $2 \pi$-periodic solutions for Duffing equations

\begin{equation*}x'' +cx' + g(t,x) = s(1+h(t)) \end{equation*}

under the condition of nonuniform non-resonance related to the positive asymptotic behavior of $g(t,x)x ^{-1}$ at the first two eigenvalues $0$ and $1$ of the periodic BVP on $[0,2 \pi]$ for the linear operator $L = - x''$, and the condition on the negative asymptotic behavior of $g(t,x)$ at infinity. The techniques we use are degree theory and the upper and lower solution method.

References:

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M.A. DEL PINO, R.F. MANÁSEVICH AND A.MONTERO, $T$-periodic solutions for some second order differential equations with singularities, Proceedings of the Royal Society of Edinburgh 120A (1992), pp 231-243. MR 93c:34091

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J.MAWHIN AND J.R. WARD, Nonuniform non-resonance conditions at the two first eigenvalues for periodic solutions of forced Lienárd and Duffing equations, Rocky Mountain J. of Mathematics 12(1982), pp 643-654. MR 84e:34028

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Additional Information:

Chengwen Wang
Affiliation: Department of Mathematics and Computer Science Rutgers University, Newark, New Jersey 07102
Email: chengwen@andromeda.rutgers.edu

DOI: 10.1090/S0002-9939-98-04520-1
PII: S 0002-9939(98)04520-1
Received by editor(s): November 20, 1996
Communicated by: Hal L. Smith
Copyright of article: Copyright 1998, American Mathematical Society

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