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
