The existence of eigenvalues embedded in the continuous spectrum of ordinary differential operators

Abstract

SynopsisIn answer to two questions raised by W. N. Everitt, we show that, givenp> l and any countably infinite set of isolated points on the positive λ-axis, there is aq(x)inLp(0, ∞) for which the set of points constitutes the point-continuous spectrum associated with the equationy”(x) + {λ − q(x)}y(x) = 0 (0≦x<∞)and some homogeneous boundary condition atx= 0.