THE DEFORMATIONS PROBLEM FOR THE STIELTJES STRINGS SYSTEM WITH A NONLINEAR CONDITION

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.

Automated summary

In this paper, we investigate the deformations process for the Stieltjes strings system located along a geometric star-shaped graph under the influence of an external force. We consider the case where the force can be concentrated at separate points, including a node of the graph. Using variational methods, we establish the necessary and sufficient conditions for the extremum of an energy functional, prove existence and uniqueness theorems for the solution, obtain an explicit formula for the solution, and study the dependence of the solution on the length of the limiter.