A limit-point criterion for expressions with oscillatory coefficients

Thomas Thornton Read

Vol. 66 (1976), No. 1, 243–255

DOI: 10.2140/pjm.1976.66.243

Abstract

A criterion is given for the equation −(py′)′ + qy = 0 to have a solution on the interval [a,∞) which is not in L₂(a,∞). The criterion permits q (or Re q if q is complex-valued) to be decomposable into a sum q = q₁ + q₂ where the expression −(py′)′ + q₁y essentially satisfies the well-known limit-point criterion of Levinson and q₂ may be thought of as an oscillatory function whose amplitude may be large, but whose integral over [a,x] increases relatively slowly as a function of x.

Mathematical Subject Classification 2000

Primary: 34C10

Milestones

Received: 24 April 1975

Revised: 12 April 1976

Published: 1 September 1976