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In this paper, we study a model of deformations of a beam with elastic supports and nonlinear boundary conditions under the influence of an external force. The case when the force can be concentrated at separate points is considered. The minimization problem of the potential energy functional with a constraint on the displacement of the beam end is investigated. The correctness of the model is established, and the necessary and sufficient conditions for the minimum of the potential energy functional are proved. [ABSTRACT FROM AUTHOR]

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]