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Unbounded solutions of quasi-linear difference equations

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Title: Unbounded solutions of quasi-linear difference equations
Authors: Cecchi, M.1 cecchi@det.unifi.it, Došlá, Z.2 dosla@math.muni.cz, Marini, M.1 marini@ing.unifi.it
Source: Computers & Mathematics with Applications. Mar2003, Vol. 45 Issue 6-9, p1113. 11p.
Subjects: Difference equations, Asymptotic expansions, Differential-difference equations, Hypothesis, Integral theorems
Abstract: We study positive increasing solutions of the nonlinear difference equation δ(anφp(δχn))=bnf(χn+1, φp(u)=&z.sfnc;u&z.sfnc;p-2u, p>1 where {an}, {bn} are positive real sequences for n ≥ 1, fR → R is continuous with uf(u) > 0 for u ≠ 0. A full characterization of limit behavior of all these solutions in terms of an, bn is established. Examples, showing the essential role of used hypotheses, are also included. The tools used are the Schauder fixed-point theorem and a comparison method based on the reciprocity principle. [Copyright &y& Elsevier]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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.)
Database: Engineering Source
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  Data: Unbounded solutions of quasi-linear difference equations
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  Data: <searchLink fieldCode="AR" term="%22Cecchi%2C+M%2E%22">Cecchi, M.</searchLink><relatesTo>1</relatesTo><i> cecchi@det.unifi.it</i><br /><searchLink fieldCode="AR" term="%22Došlá%2C+Z%2E%22">Došlá, Z.</searchLink><relatesTo>2</relatesTo><i> dosla@math.muni.cz</i><br /><searchLink fieldCode="AR" term="%22Marini%2C+M%2E%22">Marini, M.</searchLink><relatesTo>1</relatesTo><i> marini@ing.unifi.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Mar2003, Vol. 45 Issue 6-9, p1113. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Difference+equations%22">Difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink><br /><searchLink fieldCode="DE" term="%22Differential-difference+equations%22">Differential-difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis%22">Hypothesis</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+theorems%22">Integral theorems</searchLink>
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  Data: We study positive increasing solutions of the nonlinear difference equation δ(anφp(δχn))=bnf(χn+1, φp(u)=&z.sfnc;u&z.sfnc;p-2u, p>1 where <F>{an}, {bn}</F> are positive real sequences for <F>n ≥ 1, fR → R</F> is continuous with <F>uf(u) > 0</F> for <F>u ≠ 0</F>. A full characterization of limit behavior of all these solutions in terms of <F>an, bn</F> is established. Examples, showing the essential role of used hypotheses, are also included. The tools used are the Schauder fixed-point theorem and a comparison method based on the reciprocity principle. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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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        Value: 10.1016/S0898-1221(03)00069-5
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      – SubjectFull: Asymptotic expansions
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      – SubjectFull: Differential-difference equations
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              Text: Mar2003
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