On the Control of the Spectra of Upper Strong Oscillation Exponents of Signs, Zeros, and Roots of Third-Order Differential Equations

Abstract

We construct an example of a third-order linear homogeneous differential equation with continuous coefficients on the half-line whose spectra of upper strong oscillation exponents of the signs, zeros, and roots coincide with a given Souslin set containing zero in the nonnegative half-line of the extended real line.