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Asymptotics for higher order differential equations with a middle term

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Title: Asymptotics for higher order differential equations with a middle term
Authors: Bartušek, M.1 bartusek@math.muni.cz, Cecchi, M.2 mariella.cecchi@unifi.it, Došlá, Z.1 dosla@math.muni.cz, Marini, M.2 mauro.marini@unifi.it
Source: Journal of Mathematical Analysis & Applications. Apr2012, Vol. 388 Issue 2, p1130-1140. 11p.
Subjects: Differential equations, Perturbation theory, Linear systems, Iterative methods (Mathematics), Monotone operators, Existence theorems
Abstract: Abstract: We study the higher order differential equations with a middle term as a perturbation of the linear equation Using an iterative method, we show that for every solution y of (⁎⁎), there exists a solution x of (⁎) such that () have bounded variation in a neighborhood of infinity and tend to zero. The existence of monotone solutions and bounded solutions for (⁎) is also examined. The cases are considered in detail and there are given conditions for the existence of bounded oscillatory solutions of (⁎) with an analogous asymptotic behavior to corresponding oscillatory solutions of (⁎⁎). Our results are new also in the linear case. [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Apr2012, Vol. 388 Issue 2, p1130-1140. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Monotone+operators%22">Monotone operators</searchLink><br /><searchLink fieldCode="DE" term="%22Existence+theorems%22">Existence theorems</searchLink>
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  Data: Abstract: We study the higher order differential equations with a middle term as a perturbation of the linear equation Using an iterative method, we show that for every solution y of (⁎⁎), there exists a solution x of (⁎) such that () have bounded variation in a neighborhood of infinity and tend to zero. The existence of monotone solutions and bounded solutions for (⁎) is also examined. The cases are considered in detail and there are given conditions for the existence of bounded oscillatory solutions of (⁎) with an analogous asymptotic behavior to corresponding oscillatory solutions of (⁎⁎). Our results are new also in the linear case. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Linear systems
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      – SubjectFull: Iterative methods (Mathematics)
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