Fourth‐Order Differential Equation with Deviating Argument

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2012 Italy English Publisher:WileyJournal:Abstract and Applied Analysis, volume 2,012 (issn: 1085-3375, eissn: 1687-0409,

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Authors: M. Bartusek; CECCHI, MARIELLA; Z. Dosla; MARINI, MAURO;

doi: 10.1155/2012/185242

handle: 2158/891731

Fourth‐Order Differential Equation with Deviating Argument

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Abstract

We consider the fourth‐order differential equation with middle‐term and deviating argument x(4)(t) + q(t)x(2)(t) + r(t)f(x(φ(t))) = 0, in case when the corresponding second‐order equation h″ + q(t)h = 0 is oscillatory. Necessary and sufficient conditions for the existence of bounded and unbounded asymptotically linear solutions are given. The roles of the deviating argument and the nonlinearity are explained, too.

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Italy

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Keywords

Ordinary Differential Equations, Growth, boundedness, comparison of solutions to functional-differential equations, QA1-939, Mathematics

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