Margarita Zvereva, Mikhail Kamenskii, Paul Raynaud de Fitte, Ching-Feng Wen, The deformations problem for the Stieltjes strings system with a nonlinear condition
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Volume 7, Issue 2, 1 April 2023, Pages 291-308
Abstract. 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.
How to Cite this Article:
M. Zvereva, M. Kamenskii, P. Raynaud de Fitte, C.F. Wen, The deformations problem for the Stieltjes strings system with a nonlinear condition, J. Nonlinear Var. Anal. 7 (2023), 291-308.