On the Spectral Problem of Bitsadze‐Samarskii Type and Its Application to Solving the Boundary Value Problem for a Degenerate Elliptic Equation of Fractional Order

ABSTRACT The work covers a nonlocal problem of the Bitsadze‐Samarskii type for a degenerate elliptic equation of fractional order in a vertical half‐strip . This problem connects the value of the sought function on the right boundary with its value at an internal point of the domain. Theorems on the existence and uniqueness of a solution to the problem are proved using the spectral method, with the solution constructed as a series sum over the eigenfunctions of the corresponding one‐dimensional spectral problem. The work also studied the spectral properties of a Bitsadze–Samarskii type problem for a second‐order ordinary differential equation obtained via the spectral method. Eigenvalues and the corresponding root functions are determined, their completeness and basis properties are proved, and the adjoint problem is analyzed.

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