三阶微分方程的符号、零点和根的振荡上指数的无限、无处不连续谱的存在性

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2023-10-01 DOI:10.3103/s0027132223050054

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引用次数: 0

摘要

摘要构建了两个三阶线性均质微分方程的实例，其中一个方程的符号、零点和根的振荡上强指数谱与\([0,1]\)段的有理数集重合，而另一个方程的符号、零点和根的振荡上强指数谱与\([0,1]\)段的无理数集重合。

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Existence of Infinite, Everywhere Discontinuous Spectra of Upper Exponents of Oscillation of Signs, Zeros, and Roots of Third-Order Differential Equations

Abstract

Examples of two linear homogeneous differential equations of the third order are constructed, the spectra of the upper strong exponents of oscillation of signs, zeros, and roots of one of which coincide with the set of rational numbers of the segment \([0,1]\) and those of the other equation coincide with the set of irrational numbers of the segment \([0,1]\) augmented with the number zero.

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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

期刊介绍： Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.