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The direct problem, i.e., the description of the spectrum of the Sturm-Liouville boundary value problem with a spectral parameter dependent boundary condition is investigated based on quadratic operator pencils. The corresponding inverse problem is solved. The necessary and sufficient conditions for a sequence of numbers to be the spectrum of such problem are given. An algorithm of recovering the parameters of the problem using its spectrum is proposed and the solution is unique.

Inverse Sturm-Liouville problem with a boundary condition linear in the spectral parameter