On the speed at which solutions of the Sturm-Liouville equation tend to zero

N. A. Chernyavskaya; L. A. Shuster

doi:10.1007/s40574-014-0010-0

On the speed at which solutions of the Sturm-Liouville equation tend to zero

N. A. Chernyavskaya
, L. A. Shuster

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the equation - y (x) + q (x) y (x) = f (x), x R. For a fixed p [ 1, ∞) and for a correctly solvable Eq. (1) in L p (R), we find a positive and continuous function α p (x) for x R such that we have a sharp by order equality (x) = o (α p (x)), | x | → ∞, ε y D p. Here D p = { y L p (R): y, y' A C loc (R), - y + q y L p (R) }.

Original language	English
Pages (from-to)	193-210
Number of pages	18
Journal	Bollettino dell'Unione Matematica Italiana
Volume	7
Issue number	3
DOIs	https://doi.org/10.1007/s40574-014-0010-0
State	Published - 21 Nov 2014

Bibliographical note

Publisher Copyright:
© 2014 Unione Matematica Italiana.

Keywords

Estimates of solutions
Sturm-Liouville equation

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10.1007/s40574-014-0010-0

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title = "On the speed at which solutions of the Sturm-Liouville equation tend to zero",

abstract = "We consider the equation - y (x) + q (x) y (x) = f (x), x R. For a fixed p [ 1, ∞) and for a correctly solvable Eq. (1) in L p (R), we find a positive and continuous function α p (x) for x R such that we have a sharp by order equality (x) = o (α p (x)), | x | → ∞, ε y D p. Here D p = \{ y L p (R): y, y' A C loc (R), - y + q y L p (R) \}.",

keywords = "Estimates of solutions, Sturm-Liouville equation",

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doi = "10.1007/s40574-014-0010-0",

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AU - Chernyavskaya, N. A.

AU - Shuster, L. A.

PY - 2014/11/21

Y1 - 2014/11/21

N2 - We consider the equation - y (x) + q (x) y (x) = f (x), x R. For a fixed p [ 1, ∞) and for a correctly solvable Eq. (1) in L p (R), we find a positive and continuous function α p (x) for x R such that we have a sharp by order equality (x) = o (α p (x)), | x | → ∞, ε y D p. Here D p = { y L p (R): y, y' A C loc (R), - y + q y L p (R) }.

AB - We consider the equation - y (x) + q (x) y (x) = f (x), x R. For a fixed p [ 1, ∞) and for a correctly solvable Eq. (1) in L p (R), we find a positive and continuous function α p (x) for x R such that we have a sharp by order equality (x) = o (α p (x)), | x | → ∞, ε y D p. Here D p = { y L p (R): y, y' A C loc (R), - y + q y L p (R) }.

KW - Estimates of solutions

KW - Sturm-Liouville equation

UR - https://www.scopus.com/pages/publications/84912044826

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DO - 10.1007/s40574-014-0010-0

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EP - 210

JO - Bollettino dell'Unione Matematica Italiana

JF - Bollettino dell'Unione Matematica Italiana

IS - 3

ER -

On the speed at which solutions of the Sturm-Liouville equation tend to zero

Abstract

Bibliographical note

Keywords

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