TY - JOUR
T1 - Conditions for solvability of the Hartman-Wintner problem in terms of coefficients
AU - Chernyavskaya, N. A.
AU - Shuster, L.
PY - 2003/10
Y1 - 2003/10
N2 - The Equation (1) (r(x)y′)′ = q(x)y(x) is regarded as a perturbation of (2) (r(x)z′(x))′ = q1(x)z(x). The functions r(x), q1(x) are assumed to be continuous real valued, r(x) > 0, q1(x) ≥ 0, 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), q1(x) of Equations (1) and (2) are obtained.
AB - The Equation (1) (r(x)y′)′ = q(x)y(x) is regarded as a perturbation of (2) (r(x)z′(x))′ = q1(x)z(x). The functions r(x), q1(x) are assumed to be continuous real valued, r(x) > 0, q1(x) ≥ 0, 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), q1(x) of Equations (1) and (2) are obtained.
KW - Asymptotics of solutions
KW - Differential equations of second order
KW - Hartman-Wintner problem
UR - http://www.scopus.com/inward/record.url?scp=0242319624&partnerID=8YFLogxK
U2 - 10.1017/S0013091502000263
DO - 10.1017/S0013091502000263
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AN - SCOPUS:0242319624
SN - 0013-0915
VL - 46
SP - 687
EP - 702
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
IS - 3
ER -