Fourth‐Order Differential Equation with Deviating Argument

M. Bartušek, M. Cecchi, Z. Došlá and M. Marini

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/185242

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:185242

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