TY - JOUR

T1 - On the speed at which solutions of the Sturm-Liouville equation tend to zero

AU - Chernyavskaya, N. A.

AU - Shuster, L. A.

N1 - Publisher Copyright:
© 2014 Unione Matematica Italiana.

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 - http://www.scopus.com/inward/record.url?scp=84912044826&partnerID=8YFLogxK

U2 - 10.1007/s40574-014-0010-0

DO - 10.1007/s40574-014-0010-0

M3 - Article

AN - SCOPUS:84912044826

SN - 1972-6724

VL - 7

SP - 193

EP - 210

JO - Bollettino dell'Unione Matematica Italiana

JF - Bollettino dell'Unione Matematica Italiana

IS - 3

ER -