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ASYMPTOTIC THEORY FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATIONS

ASYMPTOTIC THEORY FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATIONS DEMONSTRATIO MATHEMATICAVol. XXXINo 11998A. S. A. Al-HammadiA S Y M P T O T I C T H E O R Y FOR A CLASSOF T H I R D - O R D E R D I F F E R E N T I A L EQUATIONS1. IntroductionWe investigate the asymptotic form of three linearly independent solutions of the third-order differentialy equation( 1 . 1 )( q ( q y ' ) ' ) ' + p y ' +r y=0as χ —> oo, where χ is the independent variable and the prime denotes dx—'The coefficients q, r are nowhere zero in some interval [a, oo). In the case ofq = 1, (1.1) reduces to the equation(1.2)y"'+p y '+r y=0considered by G. W. Pfeiffer [8], who, by the following conditions(i) p, r are real-valued functions, r G C^ [α,οο) is such that r ' r " — 0 ,as χ —• oo(ii) r " r ~ z , p ' r ~ ï , p r ~ 6 ¿(α,οο),showed that (1.2) has the asymptotic results, as χ —• oo, given by2(1.3)yk{ x )~r1k3 ( a ; ) e x pwhere ω\ — —1, U2 = u>3 = http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ASYMPTOTIC THEORY FOR A CLASS OF THIRD-ORDER DIFFERENTIAL EQUATIONS

Al-Hammadi, A. S. A.
Demonstratio Mathematica , Volume 31 (1): 8 – Jan 1, 1998
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References (4)

Publisher
de Gruyter
Copyright
© by A. S. A. Al-Hammadi
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1998-0109
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXINo 11998A. S. A. Al-HammadiA S Y M P T O T I C T H E O R Y FOR A CLASSOF T H I R D - O R D E R D I F F E R E N T I A L EQUATIONS1. IntroductionWe investigate the asymptotic form of three linearly independent solutions of the third-order differentialy equation( 1 . 1 )( q ( q y ' ) ' ) ' + p y ' +r y=0as χ —> oo, where χ is the independent variable and the prime denotes dx—'The coefficients q, r are nowhere zero in some interval [a, oo). In the case ofq = 1, (1.1) reduces to the equation(1.2)y"'+p y '+r y=0considered by G. W. Pfeiffer [8], who, by the following conditions(i) p, r are real-valued functions, r G C^ [α,οο) is such that r ' r " — 0 ,as χ —• oo(ii) r " r ~ z , p ' r ~ ï , p r ~ 6 ¿(α,οο),showed that (1.2) has the asymptotic results, as χ —• oo, given by2(1.3)yk{ x )~r1k3 ( a ; ) e x pwhere ω\ — —1, U2 = u>3 =

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 1998

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