Conditions for solvability of the Hartman-Wintner problem in terms of coefficients

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Abstract

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.

Original languageEnglish
Pages (from-to)687-702
Number of pages16
JournalProceedings of the Edinburgh Mathematical Society
Volume46
Issue number3
DOIs
StatePublished - 1 Oct 2003

Keywords

  • Asymptotics of solutions
  • Differential equations of second order
  • Hartman-Wintner problem

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