Bifurcation of special periodic solutions to delay-differential equations

Summary We consider a class of forced delay differential equations in which the delay is given by /2 and investigate the problem of finding its special periodic solutions. We first approximate these by a Rayleigh-Ritz-Galerkin sequence. Our second method introduces an averaged model thought to give a qualitative approximation to the solution behavior. The effects of cubic and quintic nonlinearities are compared.

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Zusammenfassung Wir untersuchen eine Klasse von forcierten Differentialgleichungen mit Zeitverzögerung /2 und suchen nach speziellen periodischen Lösungen. Zunächst approximieren wir Lösungen durch eine Folge von Rayleigh-Ritz-Galerkin-Näherungen. Als zweite Methode benutzen wir ein Mittelungsverfahren zur qualitativen Approximation des Lösungsverhaltens. Die Effekte von Nichtlinearitäten dritter und fünfter Ordnung werden verglichen.

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Supported in part by the DAAD/CONICYT Professor Exchange Program.

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Supported in part by CONICYT (Grant 89-576) and University of Concepción (Grant 20-12-17).

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Supported in part by DICYT at the University of Santiago (Grant 16-14).     

Bifurcation of periodic solutions of periodic evolution equations in a cone

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非线性微分方程的正周期解

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Time periodic solutions of nonlinear wave equations

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