Density-Type Properties of the Space of the Solutions of an Ordinary Differential Equation

Authors

  • Farkhod Mukhamadiev National University of Uzbekistan, 4, Univeritet Street, Tashkent, Ozbekistan Kimyo International University in Tashkent, 156, Usman Nasyr street, Tashkent, Ozbekistan https://orcid.org/0000-0002-1892-4899
  • Zhyldyz Artykova Osh State University, 331, Lenin street, Osh, Kyrgyzstan https://orcid.org/0009-0005-6513-9366
  • Tursun Yuldashev Tashkent State Transport University, 1, Temiryo’lchilar Street, Tashkent, Ozbekistan V. I. Romanovskii Institute of Mathematics of Ozbekistan Academy of Science, Tashkent, Ozbekistan Osh State University, 331, Lenin street, Osh, Kyrgyzstan https://orcid.org/0000-0002-9346-5362
  • Gulbadan Matieva Osh State University, 331, Lenin street, Osh, Kyrgyzstan

Keywords:

Density, local density, weak density, local weak density, hyperspace, superextension, ordinary differential equation

Abstract

In this paper we provide a detailed analysis of the density-type properties of the
space of solutions of an ordinary differential equation. We show that the density, local density,
weak density, and local weak density of the space of solutions of an ordinary differential equation
are countable. Furthermore, we prove that these properties are preserved under functors of
hyperspace and superextensions of the space of solutions of an ordinary differential equation.

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Published

2026-01-10

Issue

No. 1 (2026): Journal of Osh State University. Differential Equations

Section

Статьи