@article{Plotnikov_Komleva_Skripnik_2024, title={Existence of basic solutions of first order linear homogeneous set-valued differential equations}, volume={61}, url={http://www.matstud.org.ua/ojs/index.php/matstud/article/view/459}, DOI={10.30970/ms.61.1.61-78}, abstractNote={<p>The paper presents various derivatives of set-valued mappings,<br>their main properties and how they are related to each other.<br>Next, we consider Cauchy problems with linear homogeneous<br>set-valued differential equations with different types of<br>derivatives (Hukuhara derivative, PS-derivative and<br>BG-derivative). It is known that such initial value problems with<br>PS-derivative and BG-derivative have infinitely many solutions.<br>Two of these solutions are called basic. These are solutions such<br>that the diameter function of the solution section is a<br>monotonically increasing (the first basic solution) or monotonically<br>decreasing (the second basic solution) function. However, the second<br>basic solution does not always exist. We provide<br>conditions for the existence of basic solutions of such initial<br>value problems. It is shown that their existence depends on the<br>type of derivative, the matrix of coefficients on the right-hand<br>and the type of the initial set. Model examples are considered.</p>}, number={1}, journal={Matematychni Studii}, author={Plotnikov, A. V. and Komleva, T. A. and Skripnik, N. V.}, year={2024}, month={Mar.}, pages={61-78} }