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In the present paper, we investigate a problem, describing the deformations process for the Stieltjes strings system located along a geometric star - shaped graph under the influence of an external force. The case when the force can be concentrated at separate points, including a node of the graph, is considered. The non-linear condition arises due to the presence of a limiter on the strings displacement in the node. Using variational methods, the necessary and sufficient conditions for the extremum of an energy functional are established; existence and uniqueness theorems for the solution are proved; an explicit formula for the solution is obtained; and the dependence solution on the length of the limiter 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]