On the Unique Solvability of the Generalized Oscillation Problem of a Beam With Closed Ends in Sobolev Classes in the Multidimensional Case With the Miller‐Ross Operator

ABSTRACT This paper establishes the existence and uniqueness of a solution to the generalized oscillation problem for a beam with closed ends. The solution is constructed as a series expansion using the eigenfunctions of a multidimensional spectral problem, where the eigenvalues are determined as the roots of a transcendental equation. It is demonstrated that the system of eigenfunctions is complete and forms a Riesz basis in Sobolev spaces.