Existence of basic solutions of first order linear homogeneous set-valued differential equations
The paper presents various derivatives of set-valued mappings, their main properties and how they are related to each other. Next, we consider Cauchy problems with linear homogeneous set-valued differential equations with different types of derivatives (Hukuhara derivative, PS-derivative and BG-deri...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2024-03-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/459 |
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| author | A. V. Plotnikov T. A. Komleva N. V. Skripnik |
| author_facet | A. V. Plotnikov T. A. Komleva N. V. Skripnik |
| author_sort | A. V. Plotnikov |
| collection | DOAJ |
| description | The paper presents various derivatives of set-valued mappings,
their main properties and how they are related to each other.
Next, we consider Cauchy problems with linear homogeneous
set-valued differential equations with different types of
derivatives (Hukuhara derivative, PS-derivative and
BG-derivative). It is known that such initial value problems with
PS-derivative and BG-derivative have infinitely many solutions.
Two of these solutions are called basic. These are solutions such
that the diameter function of the solution section is a
monotonically increasing (the first basic solution) or monotonically
decreasing (the second basic solution) function. However, the second
basic solution does not always exist. We provide
conditions for the existence of basic solutions of such initial
value problems. It is shown that their existence depends on the
type of derivative, the matrix of coefficients on the right-hand
and the type of the initial set. Model examples are considered. |
| format | Article |
| id | doaj-art-1bf419e5646149d08f2fa0429aab6d2a |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2024-03-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-1bf419e5646149d08f2fa0429aab6d2a2025-08-20T03:33:27ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202024-03-01611617810.30970/ms.61.1.61-78459Existence of basic solutions of first order linear homogeneous set-valued differential equationsA. V. Plotnikov0T. A. Komleva1N. V. Skripnik2Odessa State Academy of Civil Engineering and Architecture, Odessa, UkraineOdessa State Academy of Civil Engineering and ArchitectureOdessa I.I. Mechnikov National University, Odessa, UkraineThe paper presents various derivatives of set-valued mappings, their main properties and how they are related to each other. Next, we consider Cauchy problems with linear homogeneous set-valued differential equations with different types of derivatives (Hukuhara derivative, PS-derivative and BG-derivative). It is known that such initial value problems with PS-derivative and BG-derivative have infinitely many solutions. Two of these solutions are called basic. These are solutions such that the diameter function of the solution section is a monotonically increasing (the first basic solution) or monotonically decreasing (the second basic solution) function. However, the second basic solution does not always exist. We provide conditions for the existence of basic solutions of such initial value problems. It is shown that their existence depends on the type of derivative, the matrix of coefficients on the right-hand and the type of the initial set. Model examples are considered.http://matstud.org.ua/ojs/index.php/matstud/article/view/459set-valued mappingset-valued differential equationcauchy problemhukuhara derivative |
| spellingShingle | A. V. Plotnikov T. A. Komleva N. V. Skripnik Existence of basic solutions of first order linear homogeneous set-valued differential equations Математичні Студії set-valued mapping set-valued differential equation cauchy problem hukuhara derivative |
| title | Existence of basic solutions of first order linear homogeneous set-valued differential equations |
| title_full | Existence of basic solutions of first order linear homogeneous set-valued differential equations |
| title_fullStr | Existence of basic solutions of first order linear homogeneous set-valued differential equations |
| title_full_unstemmed | Existence of basic solutions of first order linear homogeneous set-valued differential equations |
| title_short | Existence of basic solutions of first order linear homogeneous set-valued differential equations |
| title_sort | existence of basic solutions of first order linear homogeneous set valued differential equations |
| topic | set-valued mapping set-valued differential equation cauchy problem hukuhara derivative |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/459 |
| work_keys_str_mv | AT avplotnikov existenceofbasicsolutionsoffirstorderlinearhomogeneoussetvalueddifferentialequations AT takomleva existenceofbasicsolutionsoffirstorderlinearhomogeneoussetvalueddifferentialequations AT nvskripnik existenceofbasicsolutionsoffirstorderlinearhomogeneoussetvalueddifferentialequations |