Vol. 66, No. 1, 1976

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A limit-point criterion for expressions with oscillatory coefficients

Thomas Thornton Read

Vol. 66 (1976), No. 1, 243–255
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
Authors
Thomas Thornton Read