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Abstract <p> For any finite set of nonnegative numbers containing zero, we construct a linear homogeneous differential equation of a given order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(&gt;2\)</EquationSource> </InlineEquation> with continuous coefficients on the nonnegative half-line whose spectra of characteristic frequencies and strong oscillation exponents of signs, zeros, and roots coincide with this set. </p>

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Realization of Finite Spectra of Oscillation Characteristics of Linear Homogeneous Differential Equations

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. E. Artisevich,
  • A. Kh. Stash

摘要

Abstract

For any finite set of nonnegative numbers containing zero, we construct a linear homogeneous differential equation of a given order \(>2\) with continuous coefficients on the nonnegative half-line whose spectra of characteristic frequencies and strong oscillation exponents of signs, zeros, and roots coincide with this set.