On the Periodic Problem for First-Order Equation with Deviating Argument

А.Sh. Shaldanbayev, Musabek I. Akylbaev, N.S. Zhumatayev, Manat Shomanbayeva, А.А. Shaldanbayevа

2019

Full text Open access: Gold Metadata (CSL-JSON)
DOI 10.1088/1742-6596/1172/1/012106
Data confidence 70 medium
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Abstract

In this paper, we study the spectral properties of the boundary value problem y '( x ) = λy ( α – x ), y (0) = y (2 π ), where the 0 ≤ α ≤ 2 π , λ -spectral parameter. It is known that a self-adjoint and completely continuous operator has a complete and orthogonal system of eigenvectors, and it has no other eigenvectors. If the operator is not self-adjoint, then it can have an orthonormal basis consisting of eigenvectors. In addition, in this case it can have another non-complete series of eigenvectors, this is a feature of the problem we considered.