E. V. Ocheretnyuk, V. I. Slyn'ko, “Estimates of the Volume of Solutions of Differential Equations with Hukuhara Derivative”, Mat. Zametki, 2015, Volume 97, Issue 3,Pages <nobr>440

This article is cited in 3 papers

Estimates of the Volume of Solutions of Differential Equations with Hukuhara Derivative

E. V. Ocheretnyuk^a, V. I. Slyn'ko^b

^a Cherkasy State Technological University
^b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine

Abstract: For a class of nonlinear differential equations with Hukuhara derivative, lower bounds for the volume of their solutions are obtained. A. D. Aleksandrov's classical inequalities for mixed volumes combined with the comparison method are used.

Keywords: nonlinear differential equation, Hukuhara derivative, volume of solutions of a differential equation, Aleksandrov's inequalities for mixed volumes, Lyapunov function, Hausdorff metric, Steiner's formula, Aumann integral.

UDC: 517.929.21

Received: 12.01.2014
Revised: 22.04.2014

DOI: 10.4213/mzm10601