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We study the Sturm–Liouville problem with the square of the spectral parameter in one boundary condition, the other boundary condition being homogeneous. In the presence of a multiple eigenvalue, we establish the basis property of the system of eigenfunctions without one arbitrary function with a simple eigenvalue. [ABSTRACT FROM AUTHOR]

A problem for the Bessel equation of zero order with complex physical and spectral parameters in the boundary condition is considered. We study whether the system of eigenfunctions has the basis property. [ABSTRACT FROM AUTHOR]

We consider a classical spectral problem that arises when studying the natural vibrations of a loaded rectangular membrane fixed on two sides, the load being distributed along one of the free sides. We study the completeness, minimality, and basis property of the system of eigenfunctions and establish conditions guaranteeing the equiconvergence of spectral expansions in this system and in a given basis. [ABSTRACT FROM AUTHOR]

We study issues related to the uniform convergence of the Fourier series expansions of Hölder class functions in the system of eigenfunctions corresponding to a spectral problem obtained from a mixed problem for the heat equation. We prove a theorem on the equiconvergence of these expansions with expansions in a well-known orthonormal basis. [ABSTRACT FROM AUTHOR]

We study the uniform convergence in C of the Fourier series of a Hölder function in a system of eigenfunctions corresponding to a spectral problem with squared spectral parameter in a boundary condition. We preliminarily study one more spectral problem with a spectral parameter in a boundary condition. [ABSTRACT FROM AUTHOR]

We analyze the uniform convergence of the Fourier series expansions of Hölder functions in the system of eigenfunctions of a spectral problem with squared spectral parameter in a boundary condition. To this end, we first prove a theorem on the equiconvergence of such expansions with those in a well-known orthonormal basis. [ABSTRACT FROM AUTHOR]

In the theory of the heat operator, we study a spectral problem with squared spectral parameter in the boundary condition. We construct the biorthogonal system and state a nonlocal spectral problem for a complete minimal eigenfunction system. [ABSTRACT FROM AUTHOR]

In the present paper, for part of the eigenfunction system corresponding to a spectral problem with spectral parameter in the boundary condition, we write out a spectral problem for the same differential equation with a nonlocal boundary condition that does not contain the spectral parameter. In addition, we construct the biorthogonal system. [ABSTRACT FROM AUTHOR]

The article analyzes a spectral problem arising in a mathematical model of torsional vibrations of a rod with pulleys at the ends. The well-known mathematical model describing small torsional vibrations of a rod consists of the wave equation for the rod rotation angle and the corresponding boundary conditions. The classical problem on the basis property of the system of root vectors was discussed. Eigenfunctions with distinct indices satisfy the relation which can be treated as orthogonality in the space.