CONDITIONS FOR SOLVABILITY OF THE HARTMAN–WINTNER PROBLEM IN TERMS OF COEFFICIENTS
2003 ◽
Vol 46
(3)
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pp. 687-702
Keyword(s):
AbstractThe Equation (1) $(r(x)y')'=q(x)y(x)$ is regarded as a perturbation of (2) $(r(x)z'(x))'=q_1(x)z(x)$. The functions $r(x)$, $q_1(x)$ are assumed to be continuous real valued, $r(x)>0$, $q_1(x)\ge0$, whereas $q(x)$ is continuous complex valued. A problem of Hartman and Wintner regarding the asymptotic integration of (1) for large $x$ by means of solutions of (2) is studied. Sufficiency conditions for solvability of this problem expressed by means of coefficients $r(x)$, $q(x)$, $q_1(x)$ of Equations (1) and (2) are obtained.AMS 2000 Mathematics subject classification: Primary 34E20
2005 ◽
Vol 136
(2)
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pp. 159-181
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1968 ◽
Vol 11
(1)
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pp. 61-64
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2019 ◽
pp. 450-456
1963 ◽
Vol 14
(2)
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pp. 322-322
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1955 ◽
Vol 7
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pp. 531-538
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2017 ◽
Vol 9
(1)
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pp. 22-27
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1971 ◽
Vol 12
(2)
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pp. 167-186
Keyword(s):
2010 ◽
Vol 88
(3)
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pp. 289-300
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