Existence of basic solutions of first order linear homogeneous set-valued differential equations - A. V. Plotnikov; T. A. Komleva; N. V. Skripnik (Математичні Студії)
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.