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We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.

In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space $X.$ We extend results obtained by Štefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral ${\int }_a^b\mathrm{d}\left[F\right]g$ exists if $F:[a,b]\to L\left(X\right)$ has a bounded semi-variation on $[a,b]$ and $g:[a,b]\to X$ is regulated on $[a,b].$ We prove that this integral has sense also if $F$ is regulated on $[a,b]$...

A long-time dynamic for granular materials arising in the hypoplastic theory of Kolymbas type is investigated. It is assumed that the granular hardness allows exponential degradation, which leads to the densification of material states. The governing system for a rate-independent strain under stress control is described by implicit differential equations. Its analytical solution for arbitrary inhomogeneous coefficients is constructed in closed form. Under cyclic loading by periodic pressure, finite...