On the Basis Property of the System of Eigenfunctions of a Spectral Problem with Spectral Parameter in the Boundary Condition

Abstract

In the present paper, we study basis properties of the system of eigenfunctions of the boundary value problem (1.1),(1.2) in the spaces Lp (0, l)(1< p<∞). Boundary value problems for second-and fourth-order ordinary differential operators with a spectral parameter in boundary conditions were studied in a series of papers (eg, see [1–17]). A number of problems in mathematical physics can be reduced to such problems (eg, see [2–10]). Basis properties of the system of eigenfunctions of the Sturm–Liouville problem with a spectral parameter in the boundary condition were studied in [10–16] in various function spaces, and the existence of eigenvalues, estimates of eigenvalues and eigenfunctions, and expansion theorems were considered in [1, 6, 8, 9] for fourth-order ordinary differential operators with a spectral parameter in a boundary condition.