On ordered-covering mappings and implicit differential inequalities

We define the set of ordered covering of a mapping that acts in partially ordered spaces; we suggest a method for finding the set of ordered covering of vector functions of several variables and the Nemytskii operator acting in Lebesgue spaces. We prove assertions on operator inequalities in arbitrary partially ordered spaces. We obtain conditions that use a set of ordered covering of the corresponding mapping and ensure that the existence of an element u such that f(u) ≥ y implies the solvability of the equation f(x) = y and the estimate x ≤ u for its solution. We study the problem on the existence of the minimal and least solutions. These results are used for the analysis of an implicit differential equation. For the Cauchy problem, we prove a theorem on an inequality of the Chaplygin type. © 2016, Pleiades Publishing, Ltd.

Авторы
Журнал
Номер выпуска
12
Язык
Английский
Страницы
1539-1556
Статус
Опубликовано
Том
52
Год
2016
Организации
  • 1 Derzhavin Tambov State University, Tambov, Russian Federation
  • 2 Peoples’ Friendship University of Russia, Moscow, Russian Federation
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3724/
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