The basis properties of eigenfunctions in the eigenvalue problem with a spectral parameter in the boundary condition

Abstract

Boundary value problems for second- and fourth- order ordinary differential operators with a spectral parameter in the boundary conditions have been exten- sively studied (see, eg, [1–9]). In [3–5], such problems were associated with particular physical processes. The basis properties of the system of eigenfunctions in the Sturm–Liouville problem with a spectral param- eter in the boundary conditions were studied in various function spaces in [7–9]. The existence of eigenvalues, estimate for eigenvalues and eigenfunctions, and expansion theorems for fourth-order operators with a spectral parameter in the boundary condition were con- sidered in [1, 6] … This paper deals with the basis properties in Lp(0, l) (1 < p < ∞) of the system of eigenfunctions of boundary value problem (1), (2) …