On Existence Theorems to Symmetric Functional Set-Valued Differential Equations

Symmetry

Marek T. Malinowski¹ 

[1] Department of Applied Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland;

关键词: set-valued differential equations;    existence theorems;    approximation sequences;    Gronwall–Bellman inequality;   

DOI  :  10.3390/sym13071219

来源: DOAJ

【 摘 要 】

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets. The main results contain a Peano type theorem on the existence of the solution and a Picard type theorem on the existence and uniqueness of the solution to such equations. The proofs are based on sequences of approximations that are constructed with appropriate Hukuhara differences of sets. An estimate of the magnitude of the solution’s values is provided as well. We show the closeness of the unique solutions when the equations differ slightly.

【 授权许可】

Unknown