title: General problems of integration of differential inequalities in explicit form
metadata.name: dc.contributor.author
metadata.value: Iljin, Yuriy A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-12-27T14:10:02Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-12-27T14:10:02Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Iljin Yu.A. General problems of integration of differential inequalities in explicit form. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 4, pp. 597–607.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8805
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This article examines the problem of finding in explicit form all solutions of the first-order nonstrict
  differential inequality. We use the formula of the general solution of the corresponding differential equation.
  Using the analogue of the method of arbitrary constant variation or, in other words, the straightening
  diffeomorphism, we reduce initial inequality to the simplest form x˙ 6 0 or x˙ > 0. Even in case when
  the equation is considered in a region of existence and uniqueness, we encounter several theoretical and
  practical problems. Firstly, there is the problem with the extension of solutions. Secondly, the general
  solution may consist of several functions that are set on different intervals of the region of definition of
  the equation, therefore the resulting inequality may have the solution, composed of different functions.
  In this case there are problems of the connection of solutions. The situation becomes more complicated
  when the equation has points of nonuniqueness. For such inequalities the method of comparison theorems
  is not applicable. We show how to solve such inequality and obtain some estimates on its solutions for this
  case. The result obtained in the article, provides unified approach to many theorems about differential
  inequalities existing in literature. Refs 10.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке РФФИ (грант №16-01-00452).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 4(62); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: differential inequality
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: comparison theorems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: general solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of variations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: extension of solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: nonuniqueness points
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: General problems of integration of differential inequalities in explicit form
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08-Iljin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8805/1/08-Iljin.pdf
resources.format: Adobe PDF
resources.size: 272,36 kB