Differential equations with set-valued solutions

We consider a special space of convex compact sets and introduce the notions of derivative and integral for a set-valued mapping that differ from those already known. We also consider a differential equation with set-valued right-hand side satisfying the Carathéodory conditions and prove theorems on the existence and uniqueness of its solutions. This approach, in contrast to the Kaleva approach, enables one to consider fuzzy differential equations as ordinary differential equations with set-valued solutions. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1326–1337, October, 2008.     

Periodic solutions of linear impulsive differential inclusions

We establish sufficient conditions for the existence of periodic R-solutions of linear differential inclusions with impulses at fixed times. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1287–1296, September, 2008.     

Conditions for the Existence of Basic Solutions of Linear Multivalued Differential Equations

Ukrainian Mathematical Journal - We discuss various definitions and properties of the derivatives of set-valued mappings. We also consider a linear set-valued differential equation and investigate...     

Effect of liquid media on the deformation of the surface layers of a polymer-metal pair in sliding friction

The relation between the high-elastic component of polyurethane deformation and the deformation of the surface layers of metals has been investigated for sliding friction in various media. The surface layers of polymer and metal are plastically deformed. There is a certain correlation between the coefficient of friction and the amount of deformation.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 147–149, January–February, 1970.