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In this paper, a model of deformations of a Stieltjes string with localized interactions with the environment (elastic supports and forces are concentrated at no more than countable set of points) is studied via variational methods. One of the boundary conditions is nonlinear and occurs due to a sleeve, which limits the movement of the right end of the string. The necessary and sufficient conditions for the extremum of the energy functional are established; the critical loads at which the contact of the end of the string with the sleeve occurs are determined; the dependence of the solution on the sleeve length is studied. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the initial boundary value problem describing oscillation process on a geometric graph with hysteresis type boundary conditions. The analogue of the d'Alembert formula is obtained. [ABSTRACT FROM AUTHOR]

In the present paper we investigate the initial - boundary value problems describing oscillation processes with boundary conditions of hysteresis type. Analogues of the d’Alembert formula are obtained. Some control problems are analysed and explicit forms of control functions are presented. [ABSTRACT FROM AUTHOR]

In the present paper, we show that the solution set of a fractional order semilinear differential inclusion in a Banach space has the topological structure of an Rδ-set. This result allows to apply a fixed point result for condensing multimaps to the translation multioperator along the trajectories of such inclusion and to prove the existence of solutions satisfying periodic and anti-periodic boundary value conditions. An example concerning with a fractional order feedback control system is presented. [ABSTRACT FROM AUTHOR]