Article

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

Umida BaltaevaDepartment of Applied Mathematics and Mathematical Physics Urgench State University Urgench UzbekistanUmrbek MadrakhimovDepartment of Applied Mathematics and Mathematical Physics Urgench State University Urgench UzbekistanMarjona Sh. KosimovaDepartment of Applied Mathematics National University of Uzbekistan Tashkent Uzbekistan

Mathematical Methods in the Applied Sciencesjournal2025en

ABI

Abstract

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.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Spectral Theory in Mathematical Physics

Identifiers

DOI: 10.1002/mma.70374

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