Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations

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2021-09-08
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Mark
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Bolyai Institute, University of Szeged
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Abstract
The paper studies the existence, exact multiplicity, and a structure of the set of positive solutions to the periodic problem u''=p(t)u+q(t,u)u+f (t); u(0)=u(\omega), u'(0)=u'(\omega), where p, f\in L([0,\omega]) and q : [0,\omega]\times R\to R is Carathéodory function. Obtained general results are applied to the forced non-autonomous Duffing equation u'' = p(t)u+h(t)|u|^\lambda\sgn u+f (t), with \lambda>1 and a non-negative h\in L([0,\omega]). We allow the coefficient p and the forcing term f to change their signs.
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Electronic Journal of Qualitative Theory of Differential Equations. 2021, vol. 2021, issue 62, p. 1-33.
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=9185
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en
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Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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